VITEEE 2013 Paper

Let mid-point of part PQ which is in between the axis is R (x1,y1) , then coordinates of P and Q will be (2x1,0) and (0,2y1) respectively.
∴ Equation oflinePQis

x

2x1

++

y

2y1

= 1
⇒ y = - (

y1

x1

) x + 2y1
If this line touches the ellipse

x2

a2

+

y2

b2

= 1
then it will satisfy the condition,
x2 = a2m2+b2
So, (2y1)2 = a2(

−y1

x1

)2+b2
⇒ 4y12 = {

a2y12

x12

}+b2
⇒ 4 = (

a2

x12

)+(

b2

y12

) ⇒ (

a2

x12

)+(

b2

y12

) = 4
∴ Required locus of (x1,y1) is

a2

x2

+

b2

y2

= 4