Question

find the equation to the locus of the point which is at a distance of 5 units from(4,-3)​

Answer 1

Answer:

The set of all points that are a given distance away from a point is a circle.

The equation of a circle centered at (h, k) with radius r is (x - h)^2 + (y - k)^2 = r^2.

So for your case, you have (x - 4)^2 + (y - -3)^2 = 5^2,

or

(x - 4)^2 + (y + 3)^2 = 25

Answer 2

Answer:

The equation of locus is

$x^{2} +y^{2} - 8x +6y =0$

Step-by-step explanation:

Let A = ( 4 , -3 )

Given that,

Distance = 5units

⇒ $\sqrt{(x-x_{1}) ^{2}+(y-y_{1})^{2} } = 5$

⇒ $\sqrt{(x-4)^{2} + (y+3)^{2} } = 5$

Squaring on both sides

⇒$(x-4)^{2} + (y+3)^{2} = 25$

⇒ $x^{2} - 8x+16 + y^{2} +6y + 9 =25$

⇒ $x^{2} +y^{2} - 8x +6y =0$

Hope this answer helps you.