the circle whose equation are x2+y2+c2=2ax ?

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The circles whose equations are x2+y2+c2=2ax and x2+y2+c2−2by=0 will …
Solution Verified by Toppr The two circles are x2 +y2 −2ax+c2 = 0 and x2 +y2 −2by+c2 = 0 centres: C1(a,0) C2(0,b) radii: r1 =√a2 −c2, r2 =√b2 −c2 Since, the two circles touch each other externally Therefore, C1C2 = r1 +r2 ⇒ √a2 +b2 = √a2 −c2 +√b2 −c2 ⇒ a2 +b2 = a2 −c2 +b2 −c2 +2√a2 −c2√b2 −c2 ⇒ c4 =a2b2 −c2(a2 +b2)+c4 ⇒ a2b2 =c2(a2 +b2)

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[Solved] The circles whose equations are x2 + y2 + c2 = 2ax and x2
Detailed Solution Download Solution PDF Concept: The equation of a circle with center at O (a, b) and radius r, is given by: (x – a) 2 + (y – b) 2 = r 2. If two circles touch each other externally, then the distance between their centers is equal to the sum of their radii.

https://www.sarthaks.com / 205667 / the-circles-whose-equations-are-y-2-c-2-2ax-and-2-y-2-c-2-2by-0-will-touch-one-another-externally

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The circles whose equations are x^2 + y^2 + c^2 = 2ax and x^2 + y^2 + c …
The circles whose equations are x2 + y2 + c2 = 2ax and x2 + y2 + c2 – 2by = 0 will touch one another … /a2 + 1/c2 = 1/c2 (4) None of these

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The circle whose equation is x^2 + y^2 – 2ax – ay + a^2 = 0 (a) passes …
1 Answer +1 vote answered Apr 5, 2019 by AmreshRoy (70.4k points) selected Apr 6, 2019 by Vikash Kumar Best answer The correct option (b) touches only X-axis Explanation: circle = x2 + y2 – 2ax – ay + a2 = 0 ∴ centre: [a, (a/2)] radius = √ [a2 + (a2/4) – a2] = (a/2) Here radius = y co-ordinate of centre ∴ Radius = distance of centre from x axis

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https://socratic.org/questions/if-the-circles-x-2-y-2-2ax-c-2-0-and-x-2-y-2-2by-c-2-0-touch-externally-prove-th
If the circles x^2+y^2+2ax+c^2=0 and x^2+y^2+2by+c^2=0 touch … – Socratic
As the two given circles touch externally, the distance between their centers C1C2 will be equal to sum of their radii. C1C2 = r1 +r2 ⇒ √a2 +b2 = √a2 − c2 +√b2 −c2 Squaring both sides we get a2 +b2 = a2 − c2 +b2 − c2 + 2√a2 −c2√b2 − c2 ⇒ 2c2 = 2√a2 − c2√b2 − c2 ⇒ c4 = (a2 −c2)(b2 − c2) ⇒ c4 = a2b2 − b2c2 −a2c2 +c4 ⇒ b2c2 + a2c2 = a2b2

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If two circles x2+y2 2ax+c2=0 and x2+y2 2by+c2=0 touch each other …
Number of Common Tangents to Two Circles in Different Conditions If two circle… Question If two circles x2+y2−2ax+c2 =0 and x2+y2−2by+c2 = 0 touch each other externally, then A 1 a2+ 1 c2= 1 b2 B 1 a2+ 1 b2= 1 c2 C 1 a2+ 1 b2= 2 c2 D 1 b2+ 1 c2= 1 a2 Solution The correct option is B 1 a2+ 1 b2= 1 c2 Let S1: x2+y2−2ax+c2 =0

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mathcentre.ac.uk/resources/uploaded/mc-ty-circles-2009-1.pdf
PDF The geometry of a circle – mathcentre.ac.uk
Find the centre and radius of the circle x2 +y2 − 6x+4y − 12 = 0. Solution First, we can check that the expression on the left-hand side is quadratic, that there is no term involving xy, and that the coefficients of x2 and y2 are equal. So this is the equation of a circle. If we compare this equation with the standard +y2 +2gx …

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Prove that the circle x^2 + y^2 + 2ax + c^2 = 0 and x^2 + y^2 + 2by – Toppr
Question Prove that the circle x 2+y 2+2ax+c 2=0 and x 2+y 2+2by+c 2=0 touches each other, if a 21+ b 21 = c 21. Medium Solution Verified by Toppr (x+a) 2+y 2=( a 2−c 2) 2 x 2+(y+b) 2=( b 2−c 2) 2 If these circles touch each other distance between centres = Sum of radii

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/hs-geo-circle-expanded-equation/a/circle-equation-review

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/hs-geo-circle-expanded-equation/a/circle-equation-review
Circle equation review | Analytic geometry (article) | Khan Academy
We know that the general equation for a circle is ( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. x^2 + y^2 -4y = 21. Then complete the square for the y terms. x^2 + y^2 – 4y + 4 = 21 + 4. Then factor.

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Prove that the circle x2+y2+2ax+c2=0 and x2+y2+2by+c2=0 touches … – Toppr
Mathematics Question Prove that the circle x2 +y2 +2ax+c2 = 0 and x2 +y2 +2by+c2 = 0 touches each other, if 1 a2 + 1 b2= 1 c2. Solution Verified by Toppr (x+a)2 +y2 =(√a2 −c2)2 x2 +(y+b)2 =(√b2 −c2)2 If these circles touch each other distance between centres = Sum of radii lesoutrali bot