How do you find the focus of a parabola y 2 4ax?

Since the focus (4, 0) lies on the x-axis, the x-axis itself is the axis of the parabola. y2 = 4ax or y2= – 4ax. Since the directrix is x = – 3 and the focus is (4, 0), the parabola is to be of the form y2= 4ax with a = 4.

What is axis of parabola y 2 4ax?

The equation y2 = – 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates of the focus are (- a, 0), the equation of directrix is x = a or x – a = 0, the equation of the axis is y = 0, the axis is along negative x-axis; the length of its latus rectum is 4a and …

How do you find the Y intercept of a mirror image?

To find the reflection of the y intercept, duplicate the y value of the point and find the x distance to the AOS then travel the same distance on the other side of the AOS. In this case, the y value of the reflection of the y intercept, (0, -1) is –1, so the reflected point will also have a y value of –1.

What does AOS mean in math?

Axis of Symmetry
The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola .

What is the focal distance of a point on the parabola?

The positive number a is called the focal length of the parabola. (x−p)2=±4a(y−q), with a>0, where (p,q) is the vertex and a is the focal length.

What is the focal distance in parabola?

Focal – Distance : The distance between a point on a parabola and its focus is called its distance. Let F(a, 0) be a focusa on parabola y2=4ax.

What is the Y intercept of a parabola equation?

The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c.

What is the mirror image of 3/4 on Y axis?

Mirror image of (3,4) on y axis is (-3,+4).

What is the equation of the circle that touches the parabola?

A circle touches the parabola y 2 = 4 a x at P. It also passes through the focus of the parabola and intersects its axis at Q. If angle S P Q is 90 degrees, what is the equation of the circle? From the data we can conclude that the center of the circle lies on the axis of the parabola. A circle touches the parabola y 2 = 4 a x at P.

How do you find the point of a parabola from its focus?

Focus of parabola is ( b, 0), and its directrix is x = − b. Thus point of parabola ( b, 2 a b) is 2 b away from directrix and 2 b away from focus ( b, 0) so 4 b 2 = 4 a b, b = a

Can a straight line touch a parabola?

Straight Line Touches a Parabola. The condition for a line to be a tangent to the parabola is that and the tangent to the parabola is . Consider that the standard equation of a parabola with vertex at origin can be written as.

What is the equation to find the centre of a circle?

The centre of the circle must lie on that normal. Let $(h,k)$ be the coordinates of the centre and r be the radius of the circle. Then its equation can be written as $x^2+y^2-2hx-2ky+c=0……(i)$