Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsEllipse

A ray of light emerging from the point p(0,4) along the tangent of the ellipse x^2 25 + y^2 16 =1 and strike a circle of radius 65 units and reflected from it. The reflected ray entering inside the ellipse through the focus (-3,0) and strike lower surface of ellipse and gets reflected from it. If the reflected ray returns to the point p(0,4) , then ordinate of the centre of circle is _______

Correct answer

5

Step-by-step solution

Using reflection property of ellipse equation of reflected ray S P is 4 x+3 y=12 ......(1) Solving equation (1) with ellipse, we get A ( 75 17 ,- 32 17 ) Equation of reflected ray BS ^ is 16 x+63+48=0 ....(2) Equation of incident ray PB is y=4 ....(3) Equation of bisector of (2) and (3) with negative slope gives normal to circle at 3 which is 4 x+32 y-53=0 Point B is (- 75 4 , 4 ) , using parametric equation of line ordinate of centre is 5

Practice Ellipse on Quantrex Academy →

More from Ellipse

Consider the ellipse E given by x^2 18 + y^2 12 = 1 . Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as that of E 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let P be the point in the first quadrant where the given ellipses intersect. If is the acute a 2026Let x^2 f(a^2+7a+3) + y^2 f(3a+15) = 1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing positive function on R . If the set of all possible valu 2026The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices are x = 4 6 3 . Let H: x^2 a^2 - y^2 b^2 = 1 be a hyperbola whose eccentricity is equal to t 2026Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is 1 3 . Let P( , 0) , > 0 , be a focus of E and AB be a chord passing through P . Then th 2026Let a focus of the ellipse E: x^2 a^2 + y^2 b^2 = 1 be S(4, 0) and its eccentricity be 4 5 . If the point P(3, ) lies on E and O is the origin, then the area of POS is equal to: 2026Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 + y^2 = 36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is 2026Let an ellipse x^2 a^2 + y^2 b^2 = 1 , a < b , pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its latus rectum is : 2026 Full Ellipse list All Most Important Selected Qs for JEE Advanced PYQs