Table of Contents
How do you find the tangent of a parabola?
Equation of tangent to parabola y 2 = 4 a x ant any parametric coordinate p (t)= p ( a t 2, 2 a t) where t is a parameter and t ∈ R is given by y t = x + a t 2 . Hence 1/t is the slope of tangent at point P (t). i.e tangent is y=mx + a/m where m is the slope of the tangent.
How do you find the equation of a parabola with two circles?
Find the equation of both the circles using S + k L = 0. L is the equation of the tangent to the parabola at points of contact. Point of contact may be considered as point circles. Since point of contact comes out to be ( 4, 4) and ( 9, 6) and the equation of tangents are: 2 y = x + 4 and 3 y = x + 9
What if p is not on the straight line between A and B?
If you don’t specify that P is on the straight line between A and B, you will have an endless number of points satisfying the equation. The only condition is that the distance between P and A is 1.5 times the distance between P and B.
Which circle passes through the focus of the parabola?
C 1 is the circle which touches the parabola at Q and C 2 is the circle which touches the parabola at R. Both circles pass through the focus of the parabola. Find the radius of circle C 2
What is the Equation of Tangent to Parabola 1 (a) Point form : The equation of tangent to the given parabola at its point () is y = 2a (x + ). 2 (b) Slope form : Example : Find the tangent to the parabola whose slope is 3. 3 (c) Parametric form. The tangent to the given parabola at its point P (t), is ty = x + a.
How to find the value of Y in a tangent equation?
Draw the tangent line for the equation, y = x 2 + 3x + 1 at x=2 To find the y value, substitute the x value in given equation. y = 2 2 + 3 (2) + 1 y = 4 + 6 + 1 y = 11 Differentiate the given equation, y = x 2 + 3x + 1 dy/dx = d (x 2 + 3x + 1)/dx dy/dx = 2x+3
What is the equation of tangent in slope m form?
Equation of tangent in slope (m) form In (6) replacing t by 1/m we have y = mx + which is equation of tangent in terms of slope and the point of contact is . Thus if line y = mx + c touches parabola y2 = 4ax we must have c = a/m (comparing equation with y = mx + a/m).
Which line is parallel to the tangent line?
If the tangent line is parallel to x-axis, then slope of the line at that point is 0. So, the required point is (1, -4). If two lines are parallel, then slopes will be equal. y = 4x – 2 is the line which is parallel to the tangent line.