# Circle Questions

## What are the Intercepts cut by the circle on axes ?

Solution : The intercepts cut by the circle $$x^2 + y^2 + 2gx + 2fy + c$$ = 0 on : (i)  x-axis = 2$$\sqrt{g^2 – c}$$ (ii)  y-axis = 2$$\sqrt{f^2 – c}$$ Similar Questions What is the equation of pair of tangents to a circle ? What is the length of tangent to a …

## What is the parametric equation of circle ?

Solution : The parametric equation of circle $$x^2 + y^2$$ = $$r^2$$ are x = rcos$$\theta$$, y = rsin$$\theta$$ ; $$\theta$$ $$\in$$ [0,2$$\pi$$) and (rcos$$\theta$$, rsin$$\theta$$) are called parametric coordinates. Similar Questions What is the Director Circle of a Circle ? Find the number of common tangents to the circles $$x^2 + y^2$$ = 1 …

## What is the Director Circle of a Circle ?

Solution : The locus of the point of intersection of two perpendicular tangents to the circle is called director circle. Let P(h, k) is the point of intersection of two tangents drawn on the circle ($$x^2$$ + $$y^2$$ = $$a^2$$). Then the equation of the pair of tangents is $$SS_1 = T^2$$. i.e. ($$x^2$$ + …

## Find the number of common tangents to the circles $$x^2 + y^2$$ = 1 and $$x^2 + y^2 – 2x – 6y + 6$$ = 0.

Solution : Let $$C_1$$ be the center of circle $$x^2 + y^2$$ = 1 i.e.  $$C_1$$ = (0, 0) And $$C_2$$ be the center of circle $$x^2 + y^2 – 2x – 6y + 6$$ = 0 i.e. $$C_2$$ = (1, 3) Let $$r_1$$ be the radius of first circle and $$r_2$$ be the radius …

Solution : Let two circles are $$S_1$$ = $${x}^2 + {y}^2 + 2{g_1}x + 2{f_1}y + {c_1}$$ = 0 and $$S_2$$ = $${x}^2 + {y}^2 + 2{g_2}x + 2{f_2}y + {c_2}$$ = 0.Then Angle of intersection of two circles is cos$$\theta$$ = |$$2{g_1}{g_2} + 2{f_1}{f_2} – {c_1} – {c_2}\over {2\sqrt{{g_1}^2 + {f_1}^2 -c_1}}{\sqrt{{g_1}^2 + {f_1}^2 … ## What is the formula for the angle of intersection of two circles ? Solution : The angle between the tangents of two circles at the point of intersection of the two circles is called angle of intersection of two circles. If two circles are \(S_1$$ = $${x}^2 + {y}^2 + 2{g_1}x + 2{f_1}y + {c_1}$$ = 0 and $$S_2$$ = $${x}^2 + {y}^2 + 2{g_2}x + 2{f_2}y + … ## The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is Solution : Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r. Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center. \(\implies$$ r = k Hence, the equation of circle is $$(x – h)^2 + (y – … ## The equation of the circle passing through the foci of the ellipse \(x^2\over 16$$ + $$y^2\over 9$$ = 1 and having center at (0, 3) is

Solution : Given the equation of ellipse is $$x^2\over 16$$ + $$y^2\over 9$$ = 1 Here, a = 4, b = 3, e = $$\sqrt{1-{9\over 16}}$$ = $$\sqrt{7\over 4}$$ $$\therefore$$ foci is ($$\pm ae$$, 0) = ($$\pm\sqrt{7}$$, 0) $$\therefore$$ Radius of the circle, r = $$\sqrt{(ae)^2+b^2}$$ r = $$\sqrt{7+9}$$ = $$\sqrt{16}$$ = 4 Now, equation …