Question

If the line joining the points (-1,-4) and (3,4) is a tangent to the circle whose centre is at origin then find the point of contact of the tangent

Answer 1

Step-by-step explanation:

answer is √-42

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Answer 2

The point of contact of the tangent on the circle is equal to (4/5 , -2/5).

The tangent is formed by joining the point (-1,-4) and (3,4) .

Slope of the line = m = (4+4)/(3+1) = 2

The equation of the tangent -

y - 4 = 2(x - 3)

=> y - 4 = 2x - 6

=> y = 2x - 2

The radius of the circle will be equal to the distance of the tangent from the center of the circle (origin) .

r = 2/√5

The equation of the circle -

x² + y² = 4/5

Put y = 2x - 2 in the equation of circle to get the point of contact

=> x² + (2x - 2)² = 4/5

=> x² + 4x² + 4 -8x = 4/5

=> 25x² - 40x +16 = 0

=> x = 4/5

y = 8/5 -2 = -2/5

The point of contact of the tangent is (4/5 , -2/5).