Question

If P(4, -3) is a point that lies on the circumference of a circle on a cartesian plane with origin ‘O’ as its centre, which of the following points would lie on the circumference?​

Answer 1

Answer:

d1 +d2Let the circle be x2 + y2 + 2gx + 2fy = 0Tangent at the origin is gx + fy = 0

Answer 2

Given:

A point P(4, -3) lies on circle. The origin is the center of circle.

To find:

which of the given points will lie on the circle.

Step-by-step explanation:

Step 1 of 2

The equation of circle is given as:

$(x-h)^{2} +(y-k)^{2} =r^{2} \\\\(x-0)^{2} +(y-0)^{2} =r^{2} \\\\x^{2} +y^{2} =r^{2}$

The radius for the given circle will be:

$4^{2} +(-3)^{2} =r^{2} \\\\16+9=r^{2} \\\\r^{2} =25\\\\r=5$

Step 2 of 2

Other points that will lie on the circumference of circle are:

(i) (-4, 3) ⇒

$(-4)^{2} +3^{2} =16+9\\\\=25\\\\=5^{2}$

(ii) (-4, -3) ⇒

$(-4)^{2} +(-3)^{2} =16+9\\\\=25\\\\=5^{2}$

(iii)(4, 3) ⇒

$4^{2} +3^{2} =16+9\\\\=25\\\\=5^{2}$

Other points that will lie on the circumference of circle are (-4,3), (-4,-3), and (4,3).