If x cos α + y sin α = p is a normal to the ellipse x 2 a 2 + y 2 b 2 = 1 , then

p 2 a 2 sec 2 α + b 2 cosec 2 α = a 2 - b 2 2

p 2 a 2 cos 2 α + b 2 sin 2 α = a 2 - b 2

p 2 a 2 cos 2 α + b 2 sin 2 α = a 2 - b 2 2

p 2 a 2 sec 2 a + b 2 cosec 2 a = a 2 - b 2

The straight line ymxctouches the parabola y216x4 then the set of all the values taken by c is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 16

Equation of parabola having the extremities of its latus rectum as

(3, 4)

and

(4, 3)

is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 17

The angle of intersection of the circles

x^{2} + y^{2}

- x + y - 8 = 0

and

x^{2} + y^{2} + 2 x + 2 y - 11 = 0

is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 18

If

x \cos α + y \sin α = p

is a normal to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,

then

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 19

If

P Q

is a double ordinate of hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

such that

O P Q

is an equilateral triangle,

O

being the centre of the hyperbola, then the eccentricity

e

of the hyperbola satisfies

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 20

The conic represented by

x = 2 (\cos t + \sin t), y = 5 (\cos t - \sin t)

is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 21

The locus of point of intersection of two tangents of the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

, meeting at right angles is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 22

The locus of the point of intersection of two tangents to the parabola

y^{2} = 4 a x

, which are at right angle to one another is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 7 - Conic Sections>Exercise 2>Q 23

The minimum area of the triangle formed by any tangent to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

with the coordinate axes is

The straight line $y = m x + c,$ touches the parabola $y^{2} = 16 (x + 4)$ then the set of all the values taken by $c$ is

Important Questions on Conic Sections

Learn and Prepare for any exam you want !

The straight line y=mx+c, touches the parabola y2=16x+4 then the set of all the values taken by c is

Important Questions on Conic Sections

Learn and Prepare for any exam you want !

The straight line $y = m x + c,$ touches the parabola $y^{2} = 16 (x + 4)$ then the set of all the values taken by $c$ is