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4y+3x =25 is the tangent to the circle x^2+ y^2 = 25 at the point P(3,4). The equation of the radius of the circle that passes through P is

PLEASE SHOW SOLUTION!

User Prabhjot
by
8.1k points

1 Answer

1 vote

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)/(4) x +
(25)/(4) ← in slope- intercept form

with slope m = -
(3)/(4)

Given a line with slope m then the slope of a line perpendicular to it is


m_(perpendicular) = -
(1)/(m) = -
(1)/(-(3)/(4) ) =
(4)/(3) , thus

y =
(4)/(3) 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 =
(4)/(3) 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

User Chris Kimpton
by
8.3k points

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