3, 0) And The Line 3x + 4y = 16 Is Tangent At The Point (4, 1) To A Circle ...

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathsQuestionThe line 4x−3y=−12 is tangent at the point (−3,0) and the line 3x+4y=16 is tangent at the point (4,1) to a circle. The equation of the circle is
  1. x2+y2−2x+6y−20=0
  2. x2+y2−2x+6y−15=0
  3. x2+y2−2x−6y−15=0
  4. x2+y2+2x+6y−15=0
Ax2+y2−2x+6y−20=0Bx2+y2−2x+6y−15=0Cx2+y2−2x−6y−15=0Dx2+y2+2x+6y−15=0Open in AppSolutionVerified by Toppr

Clearly, centre C of the required circle is the point of intersection of the normals at A and B.

Was this answer helpful?7Similar QuestionsQ1Tangents drawn from the point P(1, 8) to the circle x2+y2−6x−4y−11=0 touch the circle at points A and B. The equation of the circumcircle of triangle PAB is View SolutionQ2

The diameters of a circle are along 2x+y−7=0 and x+3y−11=0 Then the equation of this circle, which also passes through (5,7) is

View SolutionQ3Find the equation of the circle which passes through the points of intersection of circles x2+y2−2x−6y+6=0 and x2+y2+2x−6y=0 and intersects the circle x2+y2+4x+6y+4=0 orthogonally.View SolutionQ4The circles x2+y2−5x+6y+15=0 and x2+y2−2x+6y+6=0 touch each otherView SolutionQ5

Tangents are drawn from the point P(1, 8) to the circle x2+y2−6x−4y−11=0 touch the circle at the point A and B, then equation of the circumcircle of the triangle PAB is

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