Question

The centre of the circle inscribed in a square formed by the lines $x^2-8x+12=0$ and $y^2-14y+45=0$ is

• A. $(4,7)$
• B. $(7,4)$
• C. $(9,4)$
• D. $(4,9)$

Answer 1

The correct option is A $(4,7)$

The center is given by the intersection of the diagonals i.e the mid -point of a diagonal.

$x^2–8x+12=0$

$⟹(x-6)(x-2)=0$

$x=2,x=6$

$y^2–14y+45=0$

$⟹(y-9)(y-5)=0$

$y=5,y=9$

$⟹A(2,5),B(2,9),C(6,9),D(6,5)$ form the square

MP of diagonal AC = $(\frac{2+6}{2},\frac{5+9}{2})=(4,7)=center$