Advertisements
Advertisements
प्रश्न
The equation of a circle with radius 5 and touching both the coordinate axes is
पर्याय
x2 + y2 ± 10x ± 10y + 5 = 0
x2 + y2 ± 10x ± 10y = 0
x2 + y2 ± 10x ± 10y + 25 = 0
x2 + y2 ± 10x ± 10y + 51 = 0
Advertisements
उत्तर
x2 + y2 ± 10x ± 10y + 25 = 0
Case I: If the circle lies in the first quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is \[x^2 + y^2 - 2ax - 2ay + a^2 = 0\].
The given radius of the circle is 5 units, i.e.
\[a = 5\].
Thus, the equation of the circle is \[x^2 + y^2 - 10x - 10y + 25 = 0\].
Case II: If the circle lies in the second quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is \[x^2 + y^2 + 2ax - 2ay + a^2 = 0\].
The given radius of the circle is 5 units, i.e.
The equation of a circle that touches both the coordinate axes and has radius a is
The equation of a circle that touches both the coordinate axes and has radius a is \[x^2 + y^2 - 2ax + 2ay + a^2 = 0\].
Hence, the required equation of the circle is x2 + y2 ± 10x ± 10y + 25 = 0.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with:
Centre (0, −1) and radius 1.
Find the centre and radius of each of the following circles:
(x − 1)2 + y2 = 4
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).
Find the equation of a circle
which touches both the axes and passes through the point (2, 1).
Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.
If the line 2x − y + 1 = 0 touches the circle at the point (2, 5) and the centre of the circle lies on the line x + y − 9 = 0. Find the equation of the circle.
Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
Show that the points (5, 5), (6, 4), (−2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.
Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
Prove that the centres of the three circles x2 + y2 − 4x − 6y − 12 = 0, x2 + y2 + 2x + 4y − 10 = 0 and x2 + y2 − 10x − 16y − 1 = 0 are collinear.
Prove that the radii of the circles x2 + y2 = 1, x2 + y2 − 2x − 6y − 6 = 0 and x2 + y2 − 4x − 12y − 9 = 0 are in A.P.
Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.
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.
Find the equation of the circle, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.
Find the equation of the circle the end points of whose diameter are the centres of the circles x2 + y2 + 6x − 14y − 1 = 0 and x2 + y2 − 4x + 10y − 2 = 0.
Find the equation of the circle circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.
The line 2x − y + 6 = 0 meets the circle x2 + y2 − 2y − 9 = 0 at A and B. Find the equation of the circle on AB as diameter.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax − b2 = 0 and x2 + 2px − q2 = 0 respectively, then write the equation of the circle with PQ as diameter.
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
The equation x2 + y2 + 2x − 4y + 5 = 0 represents
If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre 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
If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval
If the circle x2 + y2 + 2ax + 8y + 16 = 0 touches x-axis, then the value of a is
The equation of the circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is
The area of an equilateral triangle inscribed in the circle x2 + y2 − 6x − 8y − 25 = 0 is
Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is
Equation of the circle through origin which cuts intercepts of length a and b on axes is
The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.
