What is equation of a circle when centre of circle is coinciding with the origin?

We will learn how to form the equation of a circle when the centre of the circle coincides with the origin. The equation of a circle with centre at (h, k) and radius equal to a, is (x – h)2 + (y – k)2 = a2. When the centre of the circle coincides with the origin i.e., h = k = 0.

What is the equation of a line passing through the origin?

In general, therefore, the equation y = mx represents a straight line passing through the origin with gradient m. The equation of a straight line with gradient m passing through the origin is given by y = mx . Consider the straight line with equation y = 2x + 1.

What is the equation of a straight line passing through two points?

The straight line through two points will have an equation in the form y = m x + c . We can find the value of , the gradient of the line, by forming a right-angled triangle using the coordinates of the two points.

How do you find the equation of the straight line?

There are 3 steps to find the Equation of the Straight Line : 1. Find the slope of the line 2. Put the slope and one point into the “Point-Slope Formula” 3. Simplify What is the slope (or gradient) of this line? The slope is the change in height divided by the change in horizontal distance. Looking at this diagram

How do you find the value of Y when x=0?

m = 2 1 = 2. b = 1 (value of y when x=0) So: y = 2x + 1. With that equation you can now … choose any value for x and find the matching value for y. For example, when x is 1: y = 2×1 + 1 = 3. Check for yourself that x=1 and y=3 is actually on the line. Or we could choose another value for x, such as 7:

How do you find the equation with a slope of 2?

Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be – 1: So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3.

How do you find the equation of a perpendicular line?

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.