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JEE Advanced

Explore popular questions from Conic Sections for JEE Advanced. This collection covers Conic Sections previous year JEE Advanced questions hand picked by experienced teachers.

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Q 1. The equation {tex} \frac { x ^ { 2 } } { 1 - r } - \frac { y ^ { 2 } } { 1 + r } = 1 , \quad r > 1 {/tex} represents

A

an ellipse

B

a hyperbola

C

a circle

none of these

Explanation

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Q 2. The radius of the circle passing through the foci of the ellipse {tex} \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1 , {/tex} and having its centre at {tex} ( 0,3 ) {/tex} is

4

B

3

C

{tex} \sqrt { \frac { 1 } { 2 } } {/tex}

D

{tex} \frac { 7 } { 2 } {/tex}

Explanation

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Q 3. If {tex} x = 9 {/tex} is the chord of contact of the hyperbola {tex} x ^ { 2 } - y ^ { 2 } = 9 {/tex} then the equation of the corresponding pair of tangents is

A

{tex} 9 x ^ { 2 } - 8 y ^ { 2 } + 18 x - 9 = 0 {/tex}

{tex} 9 x ^ { 2 } - 8 y ^ { 2 } - 18 x + 9 = 0 {/tex}

C

{tex} 9 x ^ { 2 } - 8 y ^ { 2 } - 18 x - 9 = 0 {/tex}

D

{tex} 9 x ^ { 2 } - 8 y ^ { 2 } + 18 x + 9 = 0 {/tex}

Explanation

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Q 4. If {tex} a > 2 b > 0 {/tex} then the positive value of {tex} m {/tex} for which {tex} y = m x - b \sqrt { 1 + m ^ { 2 } } {/tex} is a common tangent to {tex} x ^ { 2 } + y ^ { 2 } = b ^ { 2 } {/tex} and {tex} ( x - a ) ^ { 2 } + y ^ { 2 } = b ^ { 2 } {/tex} is

{tex} \frac { 2 b } { \sqrt { a ^ { 2 } - 4 b ^ { 2 } } } {/tex}

B

{tex} \frac { \sqrt { a ^ { 2 } - 4 b ^ { 2 } } } { 2 b } {/tex}

C

{tex} \frac { 2 b } { a - 2 b } {/tex}

D

{tex} \frac { b } { a - 2 b } {/tex}

Explanation


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Q 5. Two circles {tex} x ^ { 2 } + y ^ { 2 } = 6 {/tex} and {tex} x ^ { 2 } + y ^ { 2 } - 6 x + 8 = 0 {/tex} are given. Then the equation of the circle through their points of intersection and the point {tex} ( 1,1 ) {/tex} is

A

{tex} x ^ { 2 } + y ^ { 2 } - 6 x + 4 = 0 {/tex}

{tex} x ^ { 2 } + y ^ { 2 } - 3 x + 1 = 0 {/tex}

C

{tex} x ^ { 2 } + y ^ { 2 } - 4 y + 2 = 0 {/tex}

D

none of these

Explanation

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Q 6. If the two circles {tex} ( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = r ^ { 2 } {/tex} and {tex} x ^ { 2 } + y ^ { 2 } - 8 x + 2 y + 8 = 0 {/tex} intersect in two distinct points, then

{tex} 2 < r < 8 {/tex}

B

{tex} r < 2 {/tex}

C

{tex} r = 2 {/tex}

D

{tex} r > 2 {/tex}

Explanation


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Q 7. The lines {tex} 2 x - 3 y = 5 {/tex} and {tex} 3 x - 4 y = 7 {/tex} are diameters of a circle of area {tex}154{/tex} sq. units. Then the equation of this circle is

A

{tex} x ^ { 2 } + y ^ { 2 } + 2 x - 2 y = 62 {/tex}

B

{tex} x ^ { 2 } + y ^ { 2 } + 2 x - 2 y = 47 {/tex}

{tex} x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 47 {/tex}

D

{tex} x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 62 {/tex}

Explanation

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Q 8. If the circles {tex} x ^ { 2 } + y ^ { 2 } + 2 x + 2 k y + 6 = 0 , x ^ { 2 } + y ^ { 2 } + 2 k y + k = 0 {/tex} intersect orthogonally, then {tex} k {/tex} is

{tex} 2 {/tex} or {tex} - \frac { 3 } { 2 } {/tex}

B

{tex} - 2 {/tex} or {tex} - \frac { 3 } { 2 } {/tex}

C

{tex}2{/tex} or {tex} \frac { 3 } { 2 } {/tex}

D

{tex} - 2 {/tex} or {tex} \frac { 3 } { 2 } {/tex}

Explanation

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Q 9. The centre of circle inscribed in square formed by the lines {tex} x ^ { 2 } - 8 x + 12 = 0 {/tex} and {tex} y ^ { 2 } - 14 y + 45 = 0 , {/tex} is

{tex} ( 4,7 ) {/tex}

B

{tex} ( 7,4 ) {/tex}

C

{tex} ( 9,4 ) {/tex}

D

{tex} ( 4,9 ) {/tex}

Explanation

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Q 10. Locus of intersection of the two perpendicular tangents to the given hyperbola is

A

auxilary circle

B

circumcircle

C

incircle 

None of these

Explanation