Question

Determine the point on the hyperbola −7x2+6y2=20closest to the point (-2, 0).

Answer 1

let (h,k) be the points.
so the equation of tangent on hyper bola at this point -7hx+6ky=20
now slope of tangent= 7h/6k.
and slope of line joining (-2,0) and (h,k)..=(0-k)/(-2-h)
both line are perpendicular as the distence is shortest.so.
(7h/6k).(-k/-2-h)=-1.
h=-12/13.
put the value in equation as both h k lies on hyperbola...
-7(-12/13)^2+6k^2=20
from here you can solve the value of k