The equation of the circumcircle of the square formed by the lines x2-8x+12=0 and y2-14y+45=0 is

Question

The equation of the circumcircle of the square formed by the lines x2-8x+12=0 and y2-14y+45=0 is (A) x2+y2-4x-7y+57=0 (B) x2+y2-8x-14y+57=0 (C) x2+y2-8x-|14 y + 5|=0 (D) 2x2+y2-8x-14y+57=0

Tardigrade Admin · Accepted Answer

The given equation of lines are (x - 2)(x - 6)=0,(y - 5)(y - 9)=0 i.e. x=2,x=6,y=5,y=9 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-jeayrouyqjae.png" /> Circle with segment joining (2,5) and (6,9) as the diameter is (x - 2)(x - 6)+(y - 5)(y - 9)=0

Q. The equation of the circumcircle of the square formed by the lines $x^{2} - 8 x + 12 = 0$ and $y^{2} - 14 y + 45 = 0$ is

$x^{2} + y^{2} - 4 x - 7 y + 57 = 0$

$x^{2} + y^{2} - 8 x - 14 y + 57 = 0$

$x^{2} + y^{2} - 8 x - ∣ 14 y + 5 ∣ = 0$

$2 x^{2} + y^{2} - 8 x - 14 y + 57 = 0$

The given equation of lines are $(x - 2) (x - 6) = 0, (y - 5) (y - 9) = 0$
i.e. $x = 2, x = 6, y = 5, y = 9$

Circle with segment joining $(2, 5)$ and $(6, 9)$ as the diameter is $(x - 2) (x - 6) + (y - 5) (y - 9) = 0$

Q. The equation of the circumcircle of the square formed by the lines x2−8x+12=0 and y2−14y+45=0 is

x2+y2−4x−7y+57=0

x2+y2−8x−14y+57=0

x2+y2−8x−∣14y+5∣=0

2x2+y2−8x−14y+57=0