Equations of tangents

Question 1

Finding equation of tangent when equation of curve and x point is given.

Answer 1

Put x value into equation and find what y is equal to.
Differentiate equation of the curve.
Put x value into the differentiated equation to get the gradient of the tangent.
Put the points and gradient into y-b=m(x-a) and get the equation of the tangent.

Question 2

Finding unknown values for when tangent is equal to curves

Answer 2

Sp find equation with y=y for tangent and curve.
Now insert into b^2-4ac = 0 equation since that what it will be for a tangent to a curve.
Then solve for unknown values