Class 11 Math - Conic Sections - MERIT YARD
Class 11 Math - Conic Sections - MERIT YARD
1 / 40What is the standard equation of a circle with center at \( (0,0) \) and radius \( r \)?
A) \( x^2 + y^2 = r^2 \)
B) \( (x-h)^2 + y^2 = r^2 \)
C) \( x^2 + (y-k)^2 = r^2 \)
D) \( x^2 - y^2 = r^2 \)
2 / 40What is the equation of a circle with center \( (h,k) \) and radius \( r \)?
A) \( x^2 + y^2 = r^2 \)
B) \( (x-h)^2 + (y-k)^2 = r^2 \)
C) \( (x+h)^2 + (y+k)^2 = r^2 \)
D) \( (x-h)^2 - (y-k)^2 = r^2 \)
3 / 40Find the exact center of the circle:
\( x^2 + y^2 = 9 \)
A) \( (9, 9) \)
B) \( (3, 3) \)
C) \( (0, 0) \)
D) \( (1, 1) \)
4 / 40Find the radius of the circle:
\( x^2 + y^2 = 16 \)
A) \( 16 \)
B) \( 8 \)
C) \( 2 \)
D) \( 4 \)
5 / 40Find the center of the circle:
\( (x-2)^2 + (y-3)^2 = 25 \)
A) \( (-2, -3) \)
B) \( (2, -3) \)
C) \( (-2, 3) \)
D) \( (2, 3) \)
6 / 40Find the radius of the circle:
\( (x-1)^2 + (y-4)^2 = 36 \)
A) \( 36 \)
B) \( 18 \)
C) \( 6 \)
D) \( 1 \)
7 / 40The set of all points in a plane equidistant from a fixed point is mathematically called a:
A) Parabola
B) Circle
C) Ellipse
D) Hyperbola
8 / 40The fixed point used to define a circle is technically called its:
A) Centre
B) Focus
C) Vertex
D) Directrix
9 / 40The standard equation of a rightward opening parabola is given by:
A) \( y^2 = 4ax \)
B) \( y^2 = -4ax \)
C) \( x^2 = 4ay \)
D) \( x^2 = -4ay \)
10 / 40The standard equation of an upward opening parabola is given by:
A) \( y^2 = 4ax \)
B) \( y^2 = -4ax \)
C) \( x^2 = 4ay \)
D) \( x^2 = -4ay \)
11 / 40The fixed point used to mathematically define a parabola is called its:
A) Centre
B) Origin
C) Node
D) Focus
12 / 40The fixed line used to mathematically define a parabola is called its:
A) Axis
B) Directrix
C) Latus Rectum
D) Tangent
13 / 40What are the coordinates of the focus of the parabola
\( y^2 = 4ax \)?
A) \( (0, a) \)
B) \( (a, 0) \)
C) \( (-a, 0) \)
D) \( (0, -a) \)
14 / 40What are the coordinates of the focus of the parabola
\( x^2 = 4ay \)?
A) \( (a, 0) \)
B) \( (-a, 0) \)
C) \( (0, -a) \)
D) \( (0, a) \)
15 / 40The equation of the directrix for the parabola
\( y^2 = 4ax \) is:
A) \( x = -a \)
B) \( y = -a \)
C) \( x = a \)
D) \( y = a \)
16 / 40What is the length of the latus rectum of the parabola
\( y^2 = 4ax \)?
A) \( a \)
B) \( 2a \)
C) \( 4a \)
D) \( 8a \)
17 / 40The exact eccentricity \( e \) of any parabola is always equal to:
A) \( 0 \)
B) \( < 1 \)
C) \( 1 \)
D) \( > 1 \)
18 / 40Find the coordinates of the focus of the parabola
\( y^2 = 8x \).
A) \( (2, 0) \)
B) \( (0, 2) \)
C) \( (4, 0) \)
D) \( (8, 0) \)
19 / 40Find the exact length of the latus rectum of
\( x^2 = 12y \).
A) \( 3 \)
B) \( 12 \)
C) \( 6 \)
D) \( 4 \)
20 / 40A conic section is mathematically obtained by the intersection of a plane with a double-napped right circular:
A) Cylinder
B) Sphere
C) Pyramid
D) Cone
21 / 40The standard equation of an ellipse with major axis along the \( x \)-axis is:
A) \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \)
B) \( x^2 + y^2 = a^2 \)
C) \( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \)
D) \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)
22 / 40The relation between \( a, b \) and \( c \) in an ellipse is given by:
A) \( c^2 = a^2 + b^2 \)
B) \( c^2 = a^2 - b^2 \)
C) \( a^2 = b^2 - c^2 \)
D) \( c = a + b \)
23 / 40The eccentricity \( e \) of an ellipse is strictly:
A) Equal to \( 1 \)
B) Greater than \( 1 \)
C) Less than \( 1 \)
D) Zero
24 / 40What is the standard formula for the eccentricity \( e \) of an ellipse?
A) \( \frac{c}{a} \)
B) \( \frac{a}{c} \)
C) \( \frac{c}{b} \)
D) \( \frac{b}{a} \)
25 / 40What is the exact length of the major axis of the ellipse
\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)?
A) \( 2a \)
B) \( 2b \)
C) \( a \)
D) \( b \)
26 / 40What is the exact length of the minor axis of the ellipse
\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)?
A) \( 2a \)
B) \( a \)
C) \( b \)
D) \( 2b \)
27 / 40The coordinates of the vertices of the standard ellipse
\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) are:
A) \( (0, \pm b) \)
B) \( (\pm a, 0) \)
C) \( (\pm c, 0) \)
D) \( (0, \pm a) \)
28 / 40What is the length of the latus rectum of the standard ellipse
\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)?
A) \( \frac{2a^2}{b} \)
B) \( \frac{b^2}{a} \)
C) \( \frac{2b^2}{a} \)
D) \( 4a \)
29 / 40In an ellipse, the sum of the distances of any point from its two foci is always:
A) Zero
B) Infinite
C) Constant
D) Decreasing
30 / 40The standard equation of a hyperbola with transverse axis along the \( x \)-axis is:
A) \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \)
B) \( \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \)
C) \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)
D) \( x^2 - y^2 = 1 \)
31 / 40The relation between \( a, b \) and \( c \) in a hyperbola is given by:
A) \( c^2 = a^2 - b^2 \)
B) \( a^2 = b^2 + c^2 \)
C) \( c = a + b \)
D) \( c^2 = a^2 + b^2 \)
32 / 40The eccentricity \( e \) of a hyperbola is strictly:
A) Less than \( 1 \)
B) Greater than \( 1 \)
C) Equal to \( 1 \)
D) Zero
33 / 40What is the exact length of the transverse axis of the hyperbola
\( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \)?
A) \( 2b \)
B) \( 2a \)
C) \( a \)
D) \( b \)
34 / 40What is the exact length of the conjugate axis of the hyperbola
\( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \)?
A) \( 2a \)
B) \( a \)
C) \( 2b \)
D) \( b \)
35 / 40The coordinates of the foci of the standard hyperbola
\( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) are:
A) \( (\pm c, 0) \)
B) \( (0, \pm c) \)
C) \( (\pm a, 0) \)
D) \( (\pm b, 0) \)
36 / 40What is the length of the latus rectum of the standard hyperbola
\( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \)?
A) \( \frac{2a^2}{b} \)
B) \( 2a \)
C) \( 4a \)
D) \( \frac{2b^2}{a} \)
37 / 40A hyperbola in which \( a = b \) is specifically and mathematically known as an:
A) Isosceles hyperbola
B) Circular hyperbola
C) Standard hyperbola
D) Equilateral hyperbola
38 / 40Find the vertices of the ellipse:
\( \frac{x^2}{25} + \frac{y^2}{9} = 1 \)
A) \( (\pm 5, 0) \)
B) \( (0, \pm 5) \)
C) \( (\pm 3, 0) \)
D) \( (0, \pm 3) \)
39 / 40Find the exact length of the major axis of the ellipse:
\( \frac{x^2}{16} + \frac{y^2}{9} = 1 \)
A) \( 4 \)
B) \( 8 \)
C) \( 16 \)
D) \( 6 \)
40 / 40The eccentricity \( e \) of a standard circle is always equal to:
A) \( 1 \)
B) Infinity
C) \( 0 \)
D) \( -1 \)
Test Analysis

Correct ✅ 0

Wrong ❌ 0

Unattempted ⚠️ 40

Accuracy 🎯 0%

Time Taken ⏱️ 00m 00s

Let's check your math skills!
🚀 MERIT YARD: JAC BOARD SPECIALIST 🚀