Home
Class 12
MATHS
Tangents P Qa n dP R are drawn at the...

Tangents `P Qa n dP R` are drawn at the extremities of the chord of the ellipse `(x^2)/(16)+(y^2)/9=1` , which get bisected at point `P(1,1)dot` Then find the point of intersection of the tangents.

Text Solution

Verified by Experts

The correct Answer is:
`((144)/(25),(144)/(25))`

Eqution of chord having midpoint P(1,1) is
`(1*x)/(16)+(1*y)/(9)-1=(1)/(16)+(1)/(9)-1`
or `(x)/(16)+(y)/(9)=(25)/(144)`
`or 9x+16y=25" (1)`
Also, line QR is chord of contact w.r.t. point (h,k).
It equations is
`(hx)/(16)+(ky)/(9)=1`
or `9hx+16ky=144 " "(2)`
Equatiosn (1) and (2) represent the same stragith line.
`:. (9h)/(9)=(16k)/(16)=(144)/(25)`
`rArr(h,k)-=((144)/(25),(144)/(25))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Tangents P Qa n dP R are drawn at the extremities of the chord of the ellipse (x^2)/(16)+(y^2)/9=1 , which get bisected at point T(1,1)dot Then find the point of intersection of the tangents.

Find the length of the chord of the ellipse x^2/25+y^2/16=1 , whose middle point is (1/2,2/5) .

Find the length of chord of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 , whose middle point is ((1)/(2),(2)/(5)) .

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

Equations of the tangent and the normal drawn at the point (6, 0) on the ellipse (x^(2))/(36) + (y^(2))/(9 )= 1 respectively are-

Tangents are drawn to the circle x^2+y^2=9 at the points where it is met by the circle x^2+y^2+3x+4y+2=0 . Find the point of intersection of these tangents.

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

Find the equations of the tangents drawn from the point (2, 3) to the ellipse 9x^2+16 y^2=144.

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.