Find the common tangent of the parabola x24ayand y24axa0

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 1>Q 38

The locus of mid points of tangents intercepted between the axes of ellipse

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

will be

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 1>Q 39

Distance between directrices of the hyperbola

x = 8 \sec θ, y = 8 \tan θ

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 1>Q 40

The equation of the parabola to which the line

m^{2} (y - 10) - m x - 1 = 0

is a tangent for any real value of

m

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 1>Q 41

If

C

is the centre and

A, B

are the two points on the conic

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

such that

∠ A C B = \frac{π}{2},

then

C A^{- 2} + C B^{- 2}

is equal to

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 1>Q 42

If the tangent at the point

P (x_{1}, y_{1})

to the parabola

y^{2} = 4 a x

meets the parabola

y^{2} = 4 a (x + b)

at

Q

and

R,

then the midpoint of

Q R

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 1>Q 43

The normals at three points

P, Q

and

R

of the parabola

y^{2} = 4 a x

meet at

(h, k)

. The centroid of the

Δ P Q R

lies on

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 1>Q 44

The asymptotes of the hyperbola

x y - 3 x + 4 y + 2 = 0

are

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 1>Q 45

If two of the normal of the parabola

y^{2} = 4 x

that passes through

(15, 12)

are

4 x + y = 72

and

3 x - y = 33

, then the third normal is

Find the common tangent of the parabola $x^{2} = 4 a y$ and $y^{2} = 4 a x (a > 0)$

Important Questions on Conic Sections

Learn and Prepare for any exam you want !

Find the common tangent of the parabola x2=4ay and y2=4ax a>0

Important Questions on Conic Sections

Learn and Prepare for any exam you want !

Find the common tangent of the parabola $x^{2} = 4 a y$ and $y^{2} = 4 a x (a > 0)$