First slide

Definition of a circle

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

Moderate

A

12
B

15
C

20
D

25

Solution

Slope of $l_{1} = \frac{1}{2}$
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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