Question

If the line $3x-2y+6=0$ meets x-axis and 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. $x^2+y^2+4x-4=0$

Hint:

Intercept form of a line $x/a + y/b = 1$ helps find axis meeting points quickly.

Answer 1

The Correct Option is B

Step 1: Concept Find the intercepts of the line to determine coordinates of points A and B.

Step 2: Meaning For $x$-intercept ($y=0$), $3x=-6 \implies A=(-2,0)$. For $y$-intercept ($x=0$), $-2y=-6 \implies B=(0,3)$.

Step 3: Analysis The radius is $AB = \sqrt{(0 - (-2))^2 + (3 - 0)^2} = \sqrt{4 + 9} = \sqrt{13}$. The circle has centre $A(-2,0)$ and radius $\sqrt{13}$.

Step 4: Conclusion Equation: $(x+2)^2 + (y-0)^2 = (\sqrt{13})^2 \implies x^2+4x+4+y^2=13 \implies x^2+y^2+4x-9=0$. Final Answer: (B)