Answer:
2nd Option is correct.
Step-by-step explanation:
Given Equation of Circle,
( x - 3 )² + ( y + 2 )² = 25
Point on circle = ( 8 , -2 )
To find: The equation of the line that is tangent to the circle at given point.
By comparing equation of circle with standard equation of circle,
( x - h )² + ( y - k )² = r²
we get,
Coordinates of center = ( 3 , -2 )
Slope of the radius line from center to point ( 8 , -2 ) = [tex]\frac{-2-(-2)}{8-3}=0[/tex]
Since, y-coordinate of radius line is same.
⇒ This line is parallel to x-axis.
We also knows that Radius and tangent are perpendicular to each other at point of contact.
⇒ Tangent is Parallel to y-axis and passes through ( 8 , -2 )
⇒ Equation of Tangent is x = 8
Therefore, 2nd Option is correct.
