Circles are drawn through the point (2,0) to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the equation of the circle be $x^2+y^2+2gx+2fy+c=0$. Since the circle passes through $(2,0)$,we have $4+4g+c=0$,so $c = -4-4g$. The intercept

Vedclass · Accepted Answer

$x^2+y^2-9x-2ky+14=0, k \in R^{+}$

Vedclass · Answer

(A) Let the equation of the circle be $x^2+y^2+2gx+2fy+c=0$. Since the circle passes through $(2,0)$,we have $4+4g+c=0$,so $c = -4-4g$. The intercept on the $X$-axis is given by $2\sqrt{g^2-c} = 5$. Squaring both sides,$4(g^2-c) = 25$. Substituting $c = -4-4g$,we get $4(g^2+4g+4) = 25$,which simplifies to $4g^2+16g+16=25$,or $4g^2+16g-9=0$. Solving for $g$,$g = \frac{-16 \pm \sqrt{256-4(4)(-9)}}{8} = \frac{-16 \pm \sqrt{256+144}}{8} = \frac{-16 \pm 20}{8}$. Thus,$g = \frac{4}{8} = 0.5$ or $g = \frac{-36}{8} = -4.5$. Since the centre $(-g, -f)$ lies in the first quadrant,$-g > 0$,so $g Then $c = -4-4(-4.5) = -4+18 = 14$. The equation is $x^2+y^2-9x+2fy+14=0$. Let $2f = -2k$,where $k \in R^{+}$,so the equation is $x^2+y^2-9x-2ky+14=0$.

Circles are drawn through the point $(2,0)$ to cut intercepts of length $5$ units on the $X$-axis. If their centre lies in the first quadrant,then their equation is

Similar Questions

The equation of the circle which touches both the axes and whose radius is $a$ is

If each of the lines $5x + 8y = 13$ and $4x - y = 3$ contains a diameter of the circle $x^2 + y^2 - 2(a^2 - 7a + 11)x - 2(a^2 - 6a + 6)y + b^3 + 1 = 0$,then:

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

The radius of the circle passing through the point $(6, 2)$ and whose two diameters are $x + y = 6$ and $x + 2y = 4$ is

The equation of the circle passing through the point $(1, 1)$ and having two diameters along the pair of lines $x^2 - y^2 - 2x + 4y - 3 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module