Question

Through point `P(-1,4)`, two perpendicular lines are drawn which intersect x-axis at Q and R. find the locus of incentre of `Delta PQR`.
A. `x^2+y^2+2x-8y-17=0`
B. `x^2-y^2 +2x-8y+17=0`
C. `x^2+y^2-2x-8y-17=0`
D. `x^2-y^2+8x-2y-17=0`

Answer 1

Correct Answer - B
Let I(h,k) be incentre.
Incentre is equidistant from all sides. By geometry, `IP=ksqrt2`

`therefore sqrt((h+1)^1+(k-4)^2)=ksqrt2`
`therefore h^2+1+2h+k^2+16-8k=2k^2`
`therefore h^2-k^2+2h-8k+17=0`