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```
P and Q are two points of the hyperbola x^2/16 - y^2/25 =1 such that segment PQ subtends a right angle at the origin O.Show that 1/OP^2 +1/OQ^2 =(3/20)^2
P and Q are two points of the hyperbola x^2/16 - y^2/25 =1 such that segment PQ subtends a right angle at the origin O.Show that 1/OP^2 +1/OQ^2 =(3/20)^2

```
10 years ago

```							Dear student,
PQ subtend 90 at origin => y=mx,y=-x/m meet hyperbola at P,Q
let m = 1
y=x reaches hyperbola at x^2/16 - x^2/25 = 1 => x= 20/3
y=-x reaches hyperbola at x^2/16 - x^2/25 = 1 => x= 20/3
OP^-2 + OQ^-2 = 1/2*(20/3)^2 + 1/2*(20/3)^2 = (3/20)^2
```
9 years ago
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