Question

lf the line $3x-2y+6=0$ meets $x$-axis, $y$-axis respectively at $A$ and $B$, then the equation of the circle with radius $AB$ and Centre at $A$ is

• A. $x^2+y^2+4x+9=0$
• B. $x^2+y^2+4x-9=0$
• C. $x^2+y^2+4x+4=0$
• D. $x^2+y^2+4x-4=0$

Answer 1

The correct option is B $x^2+y^2+4x-9=0$

Given that:

Equation of the straight line: $3x-2y+6=0$

Since, $A$ is the centre and $B$ is one end-point.

So, $A$ is the mid-point of two diameter end points.

One point is $B$ and let other be $(x,y)$

So, $-2=\frac{x+0}{2},0=\frac{y+3}{2}$

So,Co-ordinates of other end-point$=(-4,-3)$

Equation of the circle as centre $A$ is

$(x-0)(x+4)+(y-3)(y+3)=0$ (Diameter form)

or, $x^2+4x+y^2-9=0$

or, $x^2+y^2+4x-9=0$

Hence, B is the correct option.