How do you find the equation of a tangent line given two points?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

How do you find the common tangent equation?

Equation of direct common tangents is SS1 = T2 where S is the equation of one circle.

How do you find the common tangent of two parabolas?

1 Answer

1. Let the common tangent be y=mx+c.
2. Let us find the points of intersection of this with parabola y2=4ax .
3. (mx+c)2=4ax or m2x2+x(2mc−4a)+c2=0.
4. (2mc−4a)2−4m2c2=0 or 16a2−16amc=0 or a=mc (A)
5. Similarly tangency of y=mx+c with x2=4by leads to points of intersection given by.

How do you find the common tangent of a parabola and circle?

Use the formula $c=\dfrac{a}{m}$ to get one equation. Then use the fact that for the line y = mx + c to become tangent to the circle, the perpendicular distance from the centre of the circle to the line should be equal to radius of the circle to find another equation. Solve these to get values of c and m.

What is common tangent?

Definition of Common Tangent A tangent to a circle is a line that passes through exactly one point on a circle and is perpendicular to a line passing through the center of the circle. A line that is tangent to more than one circle is referred to as a common tangent of both circles.

How do you find the direct common tangent and transverse common tangent?

The direct common tangents meet on the line passing through centres and divide it externally in the ratio of the radii. The transverse common tangents meet on the line passing through centres and divide it internally in the ratio of the radii.

What are equal parabolas?

Two equal parabolas have the same vertex and their axes are at right angles.

What is the equation of the tangent to the curve y2=8x?

The tangent to the curve y 2 = 8x is y = mx + (2 / m). Hence it must satisfy xy = – 1. It has equal roots, D = 0. The equation of the common tangent is y = x + 2. Was this answer helpful?

What is the equation of tangent to the parabola y2 = 8x?

Equation of tangent to the parabola y2 = 8x is y = mx+ ma = mx+ m2…(1), (here a = 2)

What is the equation of common tangent?

So, equation of common tangent is y=x+2.