How do you transform general form of the equation of circle to standard form and vice versa?

The standard form of a circle’s equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.

How do you write the equation of a hyperbola in standard form?

The center, vertices, and asymptotes are apparent if the equation of a hyperbola is given in standard form: (x−h)2a2−(y−k)2b2=1 or (y−k)2b2−(x−h)2a2=1. To graph a hyperbola, mark points a units left and right from the center and points b units up and down from the center.

How did you derive with the standard form of the equation of the parabola which opens upward?

For parabolas that open either up or down, the standard form equation is (x – h)^2 = 4p(y – k). For parabolas that open sideways, the standard form equation is (y – k)^2 = 4p(x – h). The vertex or tip of our parabola is given by the point (h, k).

What is A and B in a hyperbola equation?

In the general equation of a hyperbola. a represents the distance from the vertex to the center. b represents the distance perpendicular to the transverse axis from the vertex to the asymptote line(s).

Which conic’s equation has 2 squares with opposite signs?

hyperbola
If the coefficients of the squared terms have opposite signs, you have a hyperbola, stop further testing. If the squared terms are multiplied by the same coefficient, you have a circle, stop testing. If none of the above apply, you have an ellipse.

How did you transform the general form to standard form of the given equation?

The equation x2 + y2 + 6x – 4y – 3 = 0, for example, is the equation of a circle. You can change this equation to the standard form by completing the square for each of the variables. The standard form for the equation of this circle is (x + 3)2 + (y – 2)2 = 16.

How does changing the value of a change the shape of the parabola?

To recap, changing a makes the parabola appear “wider” or thinner”. In other words, when |a| > 1 (absolute value of a), the graph compresses. When 0 < |a| < 1, the graph stretches. Changing b affects the location of the vertex with respect to the y-axis.

How do you solve a parabolic equation?

The solution for any quadratic equation or parabola can be found by using a little algebra and the general formula for the quadratic equation, which is : x = -b ± sqrt(b^2 – 4ac) / 2a. Figure out the coefficients a, b, and c by looking at the given formula.