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Question

Tangents are drawn from the point (3,2) to the ellipse x2+4y2=9. Find the equation to their chord of contact and the equation of the straight line joining (3,2) to the middle point of this chord of contact.

A
3y=2x
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B
y2x=0
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C
2x+y=3
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D
None of the above
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Solution

The correct option is C 3y=2x

Given equation of ellipse is x2+4y2=9

Equation of chord of contact is T=0

xx1+4yy1=9

x(3)+4y(2)=9

3x+8y=9 ......(i)

Let the middle point of chord of contact be (h,k)

Equation of chord of contact when mid point is given is T=S

hx+4ky=h2+k2 .....(ii)

Now (i) and (ii) are equation of same line

h3=4k8=h2+k29

3h=h2+k2 ......(iii)

2h=3k ......(iv)

Substituting (iv) in (iii), we get

27h=9h2+4h213h227h=0h=0,2713

If h=0, then k=0

So, the middle point of chord of contact is (0,0)

Equation of line joining (0,0) and (3,2) is

y0=2030(x0)3y=2x

Hence, proved.


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