First slide

Definition of a circle

Question

A straight line l₂ with equation x - 2y + 10 = 0 meets the circle with equation $x^{2} + y^{2} = 100$ at B in the first quadrant. A line through B perpendicular to l₁ cuts the 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 $l_{2} = - 2$
The equation of l₂ is $y = - 2 (x - 10)$
or $y + 2 x = 20$
Hence, t = 20

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