Question

Find the equation of a circle which touches y-axis at a distance of 4 units from the origin and cuts an intercept of 6 units along the positive direction of x- axis.

Answer 1

Thank you for asking this question. Here is your answer:

Given:

PQ = 6 units

OM = 4 units

QN = PN = 3 Units

CN = MO = 4 Units

CQ² = QN² + NC²

CQ = √ 3² + 4²

= 5 units

Now CQ = CM = radius = 5 units

co - ordinate of C = (5,4)

and radius = 5 units so the equation of circle would be :

(x - 5)² + (y-4)² = 5²

x² + y² - 10x - 8y + 41 - 25 = 0

x² + y² - 10x - 8y + 16 = 0

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