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Area of Triangle Using Coordinates

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Question

A straight line $l_{1}$ with equation $x - 2 y + 10 = 0$ meets the circle with equation $x^{2} + y^{2} = 100$ at B in the first quadrant. A line through B, perpendicular to $l_{1}$ cuts y-axis at $P (0, t)$ . The value of ' $t$ ' is

A

12

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B

15

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C

20

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D

25

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Solution

The correct option is C $20$

equation of $l_{1} :$ $x - 2 y + 10 = 0$
equation of $l_{1} :$ $y = \frac{1}{2} x + 5$
Slope of $l_{1} = \frac{1}{2}$
Since $l_{2}$ is perpendicular to $l_{1}$ thus,
Slope of $l_{2} = - 2$
Equation of $l_{2}, y = - 2 (x - 10)$
$\Rightarrow y + 2 x = 20$
Hence, $t = 20$

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