Equations of tangents to circle {x^2} + {y^2} = 50 at points where line x + 7 = 0 meets it, a

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10-1.Circle and System of Circles

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The equations of the tangents to the circle ${x^2} + {y^2} = 50$ at the points where the line $x + 7 = 0$ meets it, are

A

$7x \pm y + 50 = 0$

B

$7x \pm y - 5 = 0$

C

$y \pm 7x + 5 = 0$

D

$y \pm 7x - 5 = 0$

Solution

(a) Points where $x + 7 = 0$ meets the circle ${x^2} + {y^2} = 50$ are $( – 7,\;1)$ and $( – 7,\; – 1)$.

Hence equations of tangents at these points are $ – 7x \pm y = 50$ or $7x \pm y + 50 = 0$.

Standard 11

Mathematics

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