# How do you solve the system #10x^2-25y^2-100x=-160# and #y^2-2x+16=0#?

##### 1 Answer

Feb 7, 2018

Solution is

#### Explanation:

We solve them as simultaneous equations. Here second equation gives us

or

or

or

or

i.e.

When

if

Hence, only solution is

Observe that while first equation representsa hyperbola, second equation is of a parabola. As parabola touches one arm of hyperbola at

graph{(10x^2-25y^2-100x+160)(y^2-2x+16)=0 [1.375, 11.375, -1.98, 3.02]}