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Consider Two Concentric circles C 1 : x 2 +y 2 -1=0 & C 2 : x 2 +y 2 -4=0. A parabola is drawn through the points where ‘C 1 ‘ meets the X-axis & having arbitrary tangent of ‘C 2 ’ as its directrix. Then the locus of the focus of drawn parabola is ????? Please help me !! I am confused !!

Consider Two Concentric circles C1: x2+y2-1=0 & C2 : x2+y2-4=0. A parabola is drawn through the points where ‘C1‘ meets the X-axis & having arbitrary tangent of ‘C2’ as its directrix. Then the locus of the focus of drawn parabola is ?????
Please help me !! I am confused !!

Grade:12

3 Answers

akash
22 Points
9 years ago
  • see the parabola will pass through 1,0  and  -1,0......let the points tangent at c2 be 2costheta,2sintheta....take any random point h,k as focus whose locus we have to find.....as per parabolas definition...distance from any point on parabola to focus is equal to distance from that point to directrix.....use h,k onc e with 1,0 and again  with -1,0... frame and eliminate the equations
akash
22 Points
9 years ago
  • see the parabola will pass through 1,0  and  -1,0......let the points tangent at c2 be 2costheta,2sintheta....take any random point h,k as focus whose locus we have to find.....as per parabolas definition...distance from any point on parabola to focus is equal to distance from that point to directrix.....use h,k onc e with 1,0 and again  with -1,0... frame and eliminate the equations
sajid
615 Points
8 years ago
see the parabola will pass through 1,0  and  -1,0......let the points tangent at c2 be 2costheta,2sintheta....take any random point h,k as focus whose locus we have to find.....as per parabolas definition...distance from any point on parabola to focus is equal to distance from that point to directrix.....use h,k onc e with 1,0 and again  with -1,0... frame and eliminate the equations

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