Question

prove that each straight lines x =7 and y =8 touch the circle x^2 + y^2 - 4x - 6y - 12 = 0

Answer 1

centre of circle is (2,3)

radius is √2²+3³-(-12)=5

now take distance of line from centre it must be equal to the radius and prove

Answer 2

Straight lines x =7 and y =8 touch the circle  x² + y² - 4x - 6y - 12 = 0

Step-by-step explanation:

x² + y² - 4x - 6y - 12 = 0

=> x² - 4x + 4 - 4 + y² - 6y + 9 - 9  - 12 = 0

=> (x - 2)² + (y - 3)² - 25 = 0

=>  (x - 2)² + (y - 3)² = 25

=>  (x - 2)² + (y - 3)² = 5²

=> Center (2 , 3)

Radius = 5

Hence 2 + 5 = 7  => x = 7 touches the circle

3 + 5 = 8 => y = 8 touches the circle

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