Embibe Experts Solutions for Chapter: Ellipse, Exercise 4: EXERCISE-4

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Ellipse, Exercise 4: EXERCISE-4

Attempt the free practice questions on Chapter 19: Ellipse, Exercise 4: EXERCISE-4 with hints and solutions to strengthen your understanding. Beta Question Bank for Engineering: Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Ellipse, Exercise 4: EXERCISE-4 with Hints & Solutions

MEDIUM
JEE Main/Advance
IMPORTANT

The tangent at any point P of a circle x2+y2=a2 meets the tangent at a fixed point  Aa,0 in T and T is joined to B, the other end of the diameter through A, Prove that the locus of intersection of AP and BT is an ellipse whose eccentricity is 12.

MEDIUM
JEE Main/Advance
IMPORTANT

The tangent at  P4cosθ, 1611sinθ to the ellipse 16x2 +11y2 =256 is also a tangent to the circle x2+y2-2x-15=0. Find θ. Find also the equation to the common tangent.  

EASY
JEE Main/Advance
IMPORTANT

Common tangents are drawn to the parabola the ellipse y2=4x and the ellipse 3x2+8y2=48 touching the parabola at A and B and the ellipse at C and D. Find the area of the quadrilateral.

MEDIUM
JEE Main/Advance
IMPORTANT

Find the equation of the largest circle with centre 1, 0 that can be inscribed in the ellipse x2+4y2=16.

EASY
JEE Main/Advance
IMPORTANT

The tangent at a point P on the ellipse x2a2+y2b2=1 intersects the major axis in T and N in the foot of the perpendicular from P to the same axis. Show that the circle on NT as diameter intersects the auxiliary circle orthogonally.

HARD
JEE Main/Advance
IMPORTANT

The tangents from x1, y1 to the ellipse x2a2+y2b2=1 intersect at right angles. Show that the normals at the points of contact meet on the line yy1=xx1

MEDIUM
JEE Main/Advance
IMPORTANT

If the normals at the points P, Q, R with eccentric angles α, β, γ on the ellipse x2a2+y2b2=1 are concurrent, then show that sinαcosαsin2αsinβcosβsin2βsinγcosγsin2γ=0

HARD
JEE Main/Advance
IMPORTANT

Let d be the perpendicular distance from the centre of the ellipse x2a2+y2b2=1 to the tangent drawn at a point P on the ellipse. If F1 and F2 are the two foci of the ellipse, then show that PF1-PF22=4a21-b2d2