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Maths-

General

Easy

Question

The length of intercept on y– axis, by a circle whose diameter is the line joining the points (–4, 3) and (12, –1) is -

2 $\sqrt{13}$
$\sqrt{13}$
4 $\sqrt{13}$
None of these

The correct answer is: 4 $square root of 13$

Here equation of the circle
(x+ 4) (x – 12) + (y – 3) (y+ 1) = 0
or x2 + y2 – 8x – 2y – 51 = 0
Hence intercept on y– axis
= 2 $square root of f to the power of 2 end exponent minus c end root$ = 2 $square root of 1 minus left parenthesis negative 51 right parenthesis end root$ = $4 square root of 13$

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The number of common tangents that can be drawn to the circles x²+ y²– 4x – 6y – 3 = 0 and x²+ y²+ 2x + 2y + 1 = 0 is

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parallel

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