Find the Tangent Given the Point (3,-4)

Problem

Find the Tangent Given the Point *(3,−4)

Solution

1. Identify the missing information. To find the equation of a tangent line, both a specific function ƒ(x) and a point of tangency are required.

2. Assume the standard context for this specific point (3,−4) which often refers to the circle x2+y2=25

3. Differentiate the equation x2+y2=25 implicitly with respect to x

2*x+2*yd(y)/d(x)=0

4. Solve for the slope d(y)/d(x)

d(y)/d(x)=−x/y

5. Substitute the coordinates (3,−4) to find the slope m

m=−3/(−4)=3/4

6. Apply the point-slope formula y−(y_1)=m*(x−(x_1))

y−(−4)=3/4*(x−3)

7. Simplify the equation into slope-intercept form.

y+4=3/4*x−9/4

y=3/4*x−9/4−16/4

y=3/4*x−25/4

Final Answer

y=3/4*x−25/4

Want more problems? Check here!