Question

find the equation to the circle which touch the x-axis at the distance of 4 units from the origin and cut of intercept of 6 units along the positive direction

Answer 1

The circle touches x-axis at 4 units distance,
this means the point of contact can either be 4,0 or -4,0
As the intercept(which will be a chord of the circle) is on positive side(which should mean positive y-axis), circle lies above x-axis.


Chord length=6,
Distance of chord from centre=4,
Hence radius=5

Possible circles are:
${(x - + 4) }^{2} + {(y - 5)}^{2} = {5}^{2}$

Answer 2

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

If there is any confusion please leave a comment below.