find the length of tangent to the circle 2x(raise to power 2) 2y(raise to power 2) x -2y- 17=0 at (5,-3) working pls?

Robert01

6 years ago

Equation of the circle= 2x² + 2y² + x - 2y - 17= 0

Length of the tangent to the circle at the point (5,-3)≈ (x1, y1)

Length of the tangent= √(x1)² + (y1)² + 2g(x1) + 2f(y1) + c)

2x² + 2y² + x - 2y - 17= x² + y² + 2gx + 2fy + c
c= -17
2g= 1
g= ½
2f= -2
f= -1

Length of the tangent= √((5)² + (-3)² + 2(½)(5) + 2(-1)(-3) + (-17))
= √(25 + 9 + 5 + 6 - 17)
= √(45 - 17)
= √(28)
= 5.29

Oyewumiolaniran

6 years ago

I hope u can see it
The workings are shown. Length of the tangent =5 units