The points (5, 5), (6, 4), (- 2, 4) and (7, 1) all lie on a circle. circle passes through the points A, B, C. therefore, the equation of the circle: x2 + y2 + 2ax + 2by + c = 0….. (1) Substituting A...
Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on line x – 4y = 1.
The points (3, 7), (5, 5) The line x – 4y = 1…. (1) the equation of the circle: x2 + y2 + 2ax + 2by + c = 0 ….. (2) substituting the centre (-a, -b) in equation (1) we get,...
Find the equation of the circle which passes through (3, – 2), (- 2, 0) and has its centre on the line 2x – y = 3.
The line 2x – y = 3 … (1) The points (3, -2), (-2, 0) The equation of the circle: x2 + y2 + 2ax + 2by + c = 0 ….. (2) substituting the centre (-a, -b) in equation (1) we get,...
Find the equation of the circle passing through the points : (iii) (5, -8), (-2, 9) and (2, 1) (iv) (0, 0), (-2, 1) and (-3, 2)
(iii) equation of the circle: x2 + y2 + 2ax + 2by + c = 0 ….. (1) Substituting the point (5, -8) in equation (1), we get \[\begin{array}{*{35}{l}} {{5}^{2}}~+\text{ }{{\left( -\text{ }8...
Find the equation of the circle passing through the points : (i) (5, 7), (8, 1) and (1, 3) (ii) (1, 2), (3, – 4) and (5, – 6)
(i) (5, 7), (8, 1) and (1, 3) By using the standard form of the equation of the circle: x2 + y2 + 2ax + 2by + c = 0 ….. (1) Substitute the given point (5, 7) in equation (1), we get...
Find the coordinates of the centre radius of each of the following circle: (iii) $\frac{1}{2}({{x}^{2}}+{{y}^{2}})+x\cos \theta +y\sin \theta -4=0$ (iv) ${{x}^{2}}+{{y}^{2}}-ax-by=0$
The equation of the circle is (Multiply by 2 we get) \[\begin{array}{*{35}{l}} {{x}^{2}}~+\text{ }{{y}^{2}}~+\text{ }2x\text{ }cos\text{ }\theta \text{ }+\text{ }2y\text{ }sin\text{ }\theta \text{...
Find the coordinates of the centre radius of each of the following circle: \[\begin{array}{*{35}{l}} \left( \mathbf{i} \right)\text{ }{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }{{\mathbf{y}}^{\mathbf{2}}}~+\text{ }\mathbf{6x}\text{ }\text{ }-\mathbf{8y}\text{ }-\text{ }\mathbf{24}\text{ }=\text{ }\mathbf{0} \\ \left( \mathbf{ii} \right)\text{ }\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2}{{\mathbf{y}}^{\mathbf{2}}}~-\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{5y}\text{ }=\text{ }\mathbf{7} \\ \end{array}\]
(i) The equation of the circle is x2 + y2 + 6x – 8y – 24 = 0 …… (1) Since, for a circle x2 + y2 + 2ax + 2by + c = 0 …… (2) Centre = (-a, -b) So by comparing equation (1) and (2) Centre =...