Home
Class 12
MATHS
Let F1,F2 be two focii of the ellipse an...

Let `F_1,F_2` be two focii of the ellipse and PT and PN be the tangent and the normal respectively to the ellipse at point P. Then.

A

PN bisects `angle F_(1), PF_(2)`

B

PT bisects `angle F_(1)PF_(2)`

C

PT bisects angle `(180^(@)- angle F_(1)PF_(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let F1,F_2 be two focii of the ellipse and PT and PN be the tangent and the normal respectively to the ellipse at ponit P.then

Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+13=0? (a) the latus rectum of the ellipse is 1. (b) The distance between the foci of the ellipse is 4sqrt(3)dot (c) The sum of the focal distances of a point P(x , y) on the ellipse is 4. (d) Line y=3 meets the tangents drawn at the vertices of the ellipse at points P and Q . Then P Q subtends a right angle at any of its foci.

Find the equation of tangent and normal to the ellipse x^2+8y^2=33 at (-1,2).

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

Let C : x^(2) + y^(2) = 9, E : (x^(2))/(9) + (y^(2))/(4) =1 and L : y = 2x be three curves P be a point on C and PL be the perpendicular to the major axis of ellipse E. PL cuts the ellipse at point M. If equation of normal to C at point P be L : y = 2x then the equation of the tangent at M to the ellipse E is

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

Let F_1(x_1,0)" and "F_2(x_2,0) , for x_1 lt 0 " and" x_2 gt 0 , be the foci of the ellipse (x^2)/(9)+(y^2)/(8)=1 . Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of the area of the triangle MQR to area of the quadrilateral MF_1NF_2 is :

From the point A(4,3), tangent are drawn to the ellipse (x^2)/(16)+(y^2)/9=1 to touch the ellipse at B and CdotE F is a tangent to the ellipse parallel to line B C and towards point Adot Then find the distance of A from E Fdot

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :