Question

find the area of the circle whose center is at (2, -5) and tangent to the line 4x + 3y - 8 =0
a. 6π
b.3π
c.9π
d.12π

can you help me guys to understand this question? how will get it? thanks guys.

Answer 1

There is a formula for finding the distance between a point and a straight line. Here, you can use that formula to find the distance between the center of the circle and the tangent and that will be the radius of the circle. Knowing the radius and the center of the circle you can find the equation of the circle as: \((x-h)^2 + (y-k)^2 = r^2\) where (h,k) is the center of the circle and r is the radius of the circle.

Answer 2

i don't get? sorry can you guide me to understand?

Answer 3

ok?

Answer 4

The formula to find the distance 'd' between a point (p,q) and a straight line Ax+By + C = 0 is: \(\Large d = \frac{|Ap + Bq + C|}{\sqrt{A^2 + B^2}}\). That distance will be the radius 'r'.

Then plug that 'r' into: \((x-h)^2 + (y-k)^2 = r^2\) where (h,k) is (2,-5).
That will be the equation of the circle.

Answer 5

the answer is 3?

Answer 6

but we need to prove the radian?

Answer 7

Oh, sorry, I thought they were asking for the equation of the circle. They just want the area of the circle. Find the radius, then find the area of the circle: \(\pi r^2\).

Answer 8

can you show me the proper solve to i get it?

Answer 9

if it's ok with you?

Answer 10

Distance between (2,-5) and the line 4x + 3y - 8 =0 is:

\(\Large r = \frac{|(4)(2) + (3)(-5) + (-8)|}{\sqrt{4^2 + 3^2}} = \frac{|8-15-8|}{5} =
3\)

Area = \(\Large \pi r^2 = \pi * 3^2 = 9\pi\)

Answer 11

oh thanks ill get it! thankyou ranga!

Answer 12

You are welcome.