Home
Class 12
MATHS
If the tangents to the ellipse at M and ...

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 area of the triangle MQR to area of the quadrilateral MF1NF2 is

A

`3:4`

B

`4:5`

C

`5:8`

D

`2:3`

Text Solution

Verified by Experts

Equation of tangent to ellipse at M is : `(3x)/(2xx9)+(sqrt(6)y)/(8)=1`
Put y=0 as intersection will be on x-axis
`:. R-=(6,0)`
Equation of normal to parabola, at M is `sqrt((3)/(2))x+y=2sqrt((3)/(2))+(sqrt((3)/(2)))^(3)`
Put `y=0,2+(3)/(2)=(7)/(2)`
`.:. Q-=((7)/(2),0)`
`:. "Area" (DeltMQR)=(1)/(2)xx(1-(7)/(2))xxsqrt(6)=(5)/(4)` sq. units
Area of quadrilateral `(MF_(1)NF_(2))`
`2xx"Area"(DeltaF_(1)F_(2)M)`
`=2xx(1)/(4)xx2xxsqrt(6)=2sqrt(6)` sq. units
`:.` Required Ratio `=(4)/(2)=(5)/(8)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let F_(1)(x_(1),0) and F_(2)(x_(2),0) , for x_(1)lt0 and x_(2)gt0 , be the foci of the ellipse (x^(2))/(9)+(y^(2))/(8)=1 . Suppose a parabola having vertex at the orgin 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 area of the triangle MQR to area of the quadrilateral MF_(1)NF_(2) is

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

The common tangents to the circle x^(2)+y^(2)=2 and the parabola y^(2)=8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQSR is

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

The area of the triangle formed by the tangent and the normal to the parabola y^2=4a x , both drawn at the same end of the latus rectum, and the axis of the parabola is (a) 2sqrt(2)a^2 (b) 2a^2 4a^2 (d) none of these

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Qa n dQ^(prime), then Q Q ' is