Home
Class 12
MATHS
From the point A(4,3), tangent are dr...

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`

Text Solution

Verified by Experts

The correct Answer is:
`|24-4sqrt(18)|//5`
The equation of the chord of contanct is `(x)/(4)+(y)/(3)=1`
`:.` Slop of line `EF=(-3)/(4)`
The equation of line EF is `y=-(3)/(4)x+sqrt(18)`
Therefore, the distance of (4,3) from EF is `|24-4sqrt(18)|//5`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Tangents are drawn to the ellipse (x^2)/(9)+(y^2)/(5)=1 at the ends of both latusrectum. The area of the quadrilateral so formed is

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

If from a point P , tangents PQ and PR are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Tangents are drawn to the ellipse x^2+2y^2=2 , then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

Find the points on the ellipse (x^2)/4+(y^2)/9=1 on which the normals are parallel to the line 2x-y=1.

From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y^2)/9=1. Then the point of contact lies in the (a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)