Become a member to unlock this lesson How to Find the Equation of a Circle To understand how to find the equation of a circle, one needs to be familiar with the Pythagorean Theorem (hypotenuse formula). This theorem is applied to right triangles that, in the case of a circle, have their...
For example: 1. Find the equation of this circle: The center point is not marked on this circle, but we can find it fairly easily: So from this we can tell that our center point is (2, -3) and the radius is 4. (To find the radius, simply count the number of spaces from the ...
Unit Circle Examples Example 1: Does the point P (1/2, 1/2) lie on the unit circle? Solution: We know that equation of a unit circle is: x2 + y2 = 1 Substituting x = 1/2 and y = 1/2, we get: = x2 + y2 = (1/2)2 + (1/2)2 = 1/4 + 1/4 = 1/2 ≠ 1 Si...
centreattheorigin(O)ofradius1unit. x y O ByPythagoras’Theoremweseethatx 2 +y 2 =1 Thismeansthatallpointsonthe circumferenceofthiscircleare satisfiedbyitsequation. Soforexampleconsiderthe points(1,0)and(0,1)inturn. 1 2 +0 2 =10
{/eq} Developing the left-hand side of the equation gives {eq}x^2 - 2x + 1 + y^2 + 4y + 4 = 9 \implies x^2 + y^2 - 2x + 4y - 4 = 0, {/eq} which is the standard equation of the given circle. Consider now a new example. Let {eq}x^2 + y^2 + 4x - 6y -...
Another Example Circle with a center of (2, -1) and a radius of 4 Practice Problems Practice 1 What is the equation of the circle pictured on the graph below? Show Solutions Practice 2 Look at the graph below, can you express the equation of the circle in standard form? Show Soluti...
(A,B)(A,B) are the coordinates of the center point. Just be careful about the + and - signs here; for example, a circle with an equation of the form (x−3)2+(y+3)2=52(x−3)2+(y+3)2=52 will have a center point at (3,−3)(3,−3). r2r2 is the radius of ...
Example 5: Find the equation of the circle passing through the point A(2,-1) and tangent to the line x-$$ y = 1 $$.The center of the circle is on the line$$ y = - 2 x $$ 相关知识点: 试题来源: 解析 Solution:$$ ( x - 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = ...
The equation of a circle is (7.7)x2+y2=r2, where r is the radius of the circle, and the circle has its center at the origin of the x, y coordinate system. If we are dealing in three dimensions, we have an “ellipsoid”. The locus of the equation (7.8)x2/a2+y2/b2+z2/c2...
Find the equation of the normal to the curve 5xy^2 - 2x^2 = 18 at the point (1,2) How to add and subtract integers without a number line How do you find the slope of asymptotes of a hyperbola? How to find the equation of a circle?