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Standard XII

Mathematics

Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line

If a circle p...

Question

If a circle passes through the point $(3, \sqrt{\frac{7}{2}})$ and touches $x + y = 1$ and $x - y = 1$ , centre of circle lies inside the circle $x^{2} + y^{2} - 8 x + 10 y + 15 = 0$ . Coordinates of centre of circle are given by

(4, 0)

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(4, 2)

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(6, 0)

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(7, 9)

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Solution

The correct option is A $(4, 0)$
hence the option A and C is correct

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Similar questions

Q. A circle passes through point

(3, \sqrt{\frac{7}{2}})

touches the line pair

x^{2} - y^{2} - 2 x + 1 = 0

. Centre of circle liesinside the circle

x^{2} + y^{2} - 8 x + 10 y + 15 = 0 .

Co-ordinate of centre of circle is

A circle passes through the point $(3, \sqrt{\frac{7}{2}})$ and touches the line pair $x^{2} - y^{2} - 2 x + 1 = 0$ . The coordinates of the centre of the circle are

Q. The equation of the circle which passes through the point of intersection of circles

x^{2} + y^{2} - 8 x - 2 y + 7 = 0

and

x^{2} + y^{2} - 4 x + 10 y + 8 = 0

and having its centre on

y -

axis, will be

Q. The equation of the circle concentric with the circle

x^{2} + y^{2} + 8 x + 10 y - 7 = 0

and passing through the centre of the circle

x^{2} + y^{2} - 4 x - 6 y = 0

is-

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If a circle passes through the point (3,√72) and touches x+y=1 and x−y=1, centre of circle lies inside the circle x2+y2−8x+10y+15=0. Coordinates of centre of circle are given by

The correct option is A (4,0)hence the option A and C is correct

If a circle passes through the point $(3, \sqrt{\frac{7}{2}})$ and touches $x + y = 1$ and $x - y = 1$ , centre of circle lies inside the circle $x^{2} + y^{2} - 8 x + 10 y + 15 = 0$ . Coordinates of centre of circle are given by

The correct option is A $(4, 0)$
hence the option A and C is correct