AP EAPCET 2022 - 4th July Evening Shift | Circle Question 10 | Mathematics

A circle has its centre in the first quadrant and passes through $$(2,3)$$. If this circle makes intercepts of length 3 and 4 respectively on $$x=2$$ and $$y=3$$, its equation is

$$x^2+y^2+3 x-5 y+8=0$$

$$x^2+y^2-4 x-6 y+13=0$$

$$x^2+y^2-6 x-8 y+23=0$$

$$x^2+y^2-8 x-9 y+30=0$$

AP EAPCET 2022 - 4th July Evening Shift

MCQ (Single Correct Answer)

-0

The image of the point $$(3,4)$$ with respect to the radical axis of the circles $$x^2+y^2+8 x+2 y+10=0$$ and $$x^2+y^2+7 x+3 y+10=0$$ is

$$(3,4)$$

$$(-4,-3)$$

$$(4,3)$$

$$(-3,-4)$$

AP EAPCET 2022 - 4th July Morning Shift

MCQ (Single Correct Answer)

-0

The locus of centers of the circles, possessing the same area and having $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as their common tangent, is

$$12 x-16 y-15=0$$

$$3 x-4 y+\frac{11}{2}=0$$

$$12 x-16 y+15=0$$

$$3 x-4 y-\frac{11}{2}=0$$

AP EAPCET 2022 - 4th July Morning Shift

MCQ (Single Correct Answer)

-0

For any two non-zero real numbers $$a$$ and $$b$$ if this line $$\frac{x}{a}+\frac{y}{b}=1$$ is a tangent to the circle $$x^2+y^2=1$$, then which of the following is true?

$$\left(\frac{1}{a}, \frac{1}{b}\right)$$ lies inside the circle

$$(a, b)$$ lies inside the circle

$$\left(\frac{1}{a}, \frac{1}{b}\right)$$ lies on the circle

$$(a, b)$$ lies on the circle.

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