If the circle x² + y² + 2gx+2fy + c = 0 bisects the circumference of the circ x² + y² + 2g′x + 2ƒ'y + c′ = 0 then prove that 2g′(g − g′) +2ƒ'(ƒ − ƒ') = c − c

Q: If the circle x2+y2+ax+by-12=0 has the centre  at (2,3) then find a , b and radius

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Q: х? — бх + у? — 2у - 6 %3D 0

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Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: - Show that the equation of the circle passing through (1, 1) and the points of intersection of the…

A: we need to show that equation of circle passing through (1,1) and point of intersection of given two…

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

A: The point a-1, a+1 lies in the larger segment of the circle x2+y2-x-y-6=0 made by the chord whose…

Q: i æ² + y? = 30 and (x + 1)? + (y – 1)² = 6 | ii (æ + 3)? + (y – 2)² = 9 and (x + 7)? + (y + 1)? = 4…

A: (i) The given circle is: x2+y2=30        ....1x+12+y-12=6       ....2

Q: Find the equation of the circle which is touched by y = x has on the positive direction of the x -…

A: Since the required circle has its center on the x-axis,let the coordinates of the center be…

Q: Ex(6):-(H.W) Find the center and the radius of the circle whose eq x'+ y' +x+3y 7

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Q: #8. In each case, sketch the set of points determined by the given conditions (a) /2-1+i/>1 (b)…

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Q: Find the locus of the center of the circle touching the circle x\power{2} + y\power{2} − 4y - 2x = 4…

A: Let r and R be the radii of the required and the given circle,respectively.Let the center be…

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Find the range of values of m for which the line y=mx+2 cuts the circle x\power{2}+y\power{2}=1 at…

A: The length of the perpendicular from the center (0, 0) to the line is                   21+m2

Q: If the straight line x - 2y + 1 = 0 intersects the circle x² + y² = 25 at points P and Q, then…

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Q: If the radical axis of the circles x² + y² + 2 gx + 2 fy+c= 0 and 2x² + 2y² +3x+8y +2c=0 touches the…

A: The radical axis of the given circles             x2+y2+2gx+2fy+c=0and      x2+y2+(3/2)x+4y+c=0 is…

Q: A variable circle which always touches the line x + y - 2 = 0 at (1, 1) cuts the circle x2+y2 + 4x +…

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Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1…

A: We use midpoint formula here.

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

A: (1)    Given that the equation of the circle is   x2 + y2 - x - y - 6 = 0                Given point…

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: Find the locus of the midpoint of the chords of the circle x² + y² = a² which subtend a right angle…

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Q: If the straight line x-2y+1=0 intersects the circle x\power{2}+y\power{2}=25 at points P and Q,then…

A: we need to find the coordinates of the point of intersection of the tangents drawn at P and Q to the…

Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

Q: Find the number of common tangents to the circles x\power{2}+y\power{2}+2x+8y-23=0 and…

A: For x2+y2+2x+8y-23=0 ,C1≡(-1,-4),r=210for x2+y2-4x-10y+9=0,C2≡(2,5),r=25now C1C2=distance between…

Q: If the straight line x - 2y + 1 = 0 intersects the circle x² + y² = 25 at points P and Q, then find…

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Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

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Q: A variable circle which always touches the line x+y-2=0 at (1,1) cuts the circle…

A: Any circle which touches the line x+y-2=0 at (1,1) will be of the form…

Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)

Q: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

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Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…

Q: Prove that the pair of straight lines joining the origin to the points of inersection of the circles…

A: Given circlesS≡x2+y2+2gx+2fy=0S'≡x2+y2-a2=0The equation of common chord isS-S'=0or  2gx+2fy+a2=0…