Table of Contents
What is the equation of normal to a parabola?
The various equations of normal to a parabola are given below. The equations are given in point form, parametric form and slope form….Equation of Normal in Slope Form.
| Equation of Parabola | Point of Contact | Equation of Normal |
|---|---|---|
| x2 = -4ay | (2a/m, -a/m2) | y = mx – 2a – a/m2 |
How do you find the point of contact of a tangent to a parabola?
Hence, y = mx + a/m is a tangent to the parabola y2 = 4ax, whatever be the value of m. Equation (mx + c)2 = 4ax now becomes (mx – a/m)2 = 0. ⇒ x = a/m2 and y2 = 4ax ⇒ y = 2a/m. Thus the point of contact of the tangent y = mx + a/m is (a/m2, 2a/m).
What is the equation of the tangent at a specific point of Y 2 4ax at 0 0?
Therefore, the required tangent to the parabola (1) at (0, 0) is the y-axis and hence the required equation of the tangent is x = 0.
How many number of normal equation are associated with parabola?
From a given point, a total of three normals can be drawn to the parabola y2 = 4ax.
How do you find the common normal equation?
- A. x=y.
- B. x=0.
- C. y=0.
- D. x+y=0.
How do you find the point of contact of a tangent and hyperbola?
Hi A point of contact between a tangent and a circle is the only point touching the circle by this line, The point can be found either by : equating the equations; The line : y = mx +c The circle : (x-a)^2 + (y_b)^2 = r^2 The result will be the value of {x}which can be substituted in the equation of the line to find …
How do you find the point of contact between tangent and ellipse?
Point of contact of the tangent to an ellipse Line y = mx ∓ √[a2m2 + b2] touches the ellipse x2 / a2 + y2 / b2 = 1 at (∓a2m / √[a2m2 + b2]) , (∓b2 / √[a2m2 + b2]).
Which of the following line can be a normal to the parabola y2 12x?
1,3,4 The equation of normal to the parabola y2=12x having slope m is y=mx-6m-3m3. Options (1), (3) and (4) are normal for m=-1,-2, and 3, respectively.
What is foot of normal in parabola?
The line perpendicular to the tangent of the parabola at the point of contact is called the normal.