A circle passes through points (- 1, 1) , (0, 6) and (5, 5) . point (s) on this circle, tangent (s)

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10-1.Circle and System of Circles

normal

A circle passes through the points $(- 1, 1) , (0, 6)$ and $(5, 5)$ . The point$(s)$ on this circle, the tangent$(s)$ at which is/are parallel to the straight line joining the origin to its centre is/are :

$(1, - 5)$

$(5, 1)$

$(- 1, 5)$

$(B)$ or $(C)$ both

Solution

Note that $\Delta$ is right angled at $(0, 6)$ . Centre of the circle is $(2, 3)$ . Slope of the line joining origin to the centre is $3/2$. Take parametric equation of a line through $(2, 3)$ with $tan \theta = – \frac{2}{3}$ as $\frac{{x\,\, – \,\,2}}{{\cos \,\theta }} = \frac{{y\,\, – \,\,3}}{{\sin \,\theta }} = \pm \,r $ where $r = \sqrt{13}$.

Get the co-ordinates on the circle

Standard 11

Mathematics

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A circle passes through the points $(- 1, 1) , (0, 6)$ and $(5, 5)$ . The point$(s)$ on this circle, the tangent$(s)$ at which is/are parallel to the straight line joining the origin to its centre is/are :

Solution

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