Question

ind The equation of the tangent to the curve x^2+y^2=25 at x=3

Answer 1

@experimentX : hey friend are u there ?

Answer 2

use implicit differentiation to find the slope of the tangent

Answer 3

lol,@exraven : are u there ? :DD

Answer 4

first of all, find the y axis of the point by plug in the x axis to the curve,\[x^{2} + y^{2} = 25\]\[3^{2} + y^{2} = 25\]\[y^{2} = 16\]\[y = \pm4\]therefore we have 2 points, (3,4) and (3,-4)
and then use implicit differentiation to find the slope\[2x + 2yy' = 0\]plug the points\[2(3) + 2(4)m_{1} = 0\]\[m_{1} = -\frac{3}{4}\]\[2(3) + 2(-4)m_{2} = 0\]\[m_{2} = \frac{3}{4}\]the equation of the tangent line:\[y - y_{1} = m_{1}\left( x - x_{1} \right)\]\[y - y_{2} = m_{2}\left( x - x_{2} \right)\]

Answer 5

TYSM ,U rock @exraven , :)

Answer 6

the curve is a circle with radius 5 and center (0,0). At x = 3, there are two points on the circle which give two tangent lines