Advertisements
Advertisements
प्रश्न
If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre
Advertisements
उत्तर
The equation of the circle is
x2 + y2 − 10x = 0 ...(1)
and the equation of the line is y = 2x ...(2)
Let A(x1, y1) and B(x2, y2) be the points of intersection of circle and the line.
To find the points of intersection, substitute y = 2x in 1 equation (1), we get,
x2 + 4x2 − 10x = 0
∴ 5x2 − 10x = 0
∴ x(5x − 10) = 0
∴ x = 0 or x = 2
∴ x1 = 0 and x2 = 2
Also, y1 = 2x1 and y2 = 2x2
∴ y1 = 0 and y2 = 4
∴ A ≡ (0, 0) and B ≡ (2, 4)
∴ by diameter form, the equation of the circle on chord AB as diameter is
(x − 0)(x − 2) + (y − 0)(y − 4) = 0
∴ x2 − 2x + y2 − 4y = 0
∴ x2 + y2 − 2x − 4y = 0.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)
Find the equation of the circle with centre at (a, b) touching the Y-axis
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes
Find the centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)
Choose the correct alternative:
Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0
Choose the correct alternative:
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle
Choose the correct alternative:
If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre
Choose the correct alternative:
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
Answer the following :
Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x + 10y +20 = 0,
x2 + y2 + 8x – 6y – 24 = 0.
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 10y + 19 = 0,
x2 + y2 + 2x + 8y – 23 = 0.
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 4y – 28 = 0,
x2 + y2 – 4x – 12 = 0
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 + 4x – 12y + 4 = 0,
x2 + y2 – 2x – 4y + 4 = 0
If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______
The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______
If x2 + (2h - 1)xy + y2 - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.
The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
Circle x2 + y2 – 4x = 0 touches ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the ΔPAB as P moves on the circle is ______.
The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² − y² − 2x + 4y − 3 = 0 is
