Question

The equation of the known circle is x^2+y^2-4x-4y+4=0, and the two tangents passing through the point (4 , 2) and the point (4/5 , 18/5) intersect at the point P, find the coordinates of point P.​

Answer 1

Answer:

4x - 3y = 0

Explanation:

The angle between the radius and the

tangent at P is right

The equation of a line in slope-intercept

form is

y = mx + c ( m is the slope and c the y-

intercept)

Rearrange 4y + 3x = 25 into this form

=

Subtract 3x from both sides

4y = - 3x + 25 ( divide all terms by 4)

=-

y = -- 3 x + 25 + in slope-intercept form

4

X

with slope m

--

3

4

Given a line with slope m then the slope

of a line perpendicular to it is

1

= -

= -

т

-

m perpendicular

* = 4, thus

4.

3

3

4

y = 4 x+c+ is the partial equation

To find c substitute P(3, 4) into the partial

equation

4 = 4 +C+c= 4-4 = 0

=

y = { x + equation of radius in slope-

intercept form

Multiply through by 3

3y = 4x ( subtract 3y from both sides )

=

=

4x - 3y = 0 + equation of radius in

standard form