Unit 06: Conic section

Here is the list of important questions.

  • Find the centre and radius of the circle given by the equation 4x2+4y2−8x+12y−25=0 — BSIC Gujranwala (2016)
  • Find equation of tangent to the circle x2+y2=2 parallel to the line x−2y+1=0 — BSIC Gujranwala (2016)
  • Find focus and directrix of parabola x2=−16y — BSIC Gujranwala (2016)
  • Find equation of ellipse with vertices (0,±5), eccentricity 35 — BSIC Gujranwala (2016)
  • Prove vectoprically that in any triangle ABC, a2=b2+c2−2bccosA — BSIC Gujranwala (2016)
  • Find equation of circle passing through A(4,5), B(−4,−3), C(8,−3) — BSIC Gujranwala (2016)
  • Show that the equation 9x2−18x+4y2+8y−23=0 represent an ellipse. — BSIC Gujranwala (2016)
  • Find the centre and radius of the circle x2+y2−6x+4y+13=0. — BSIC Gujranwala (2015)
  • Write the equations of tangent and normal to the circle x2+y2=25 at (4,3). — BSIC Gujranwala (2015)
  • Write the equation of parabola with focus (−3,1) and directrix x=3. — BSIC Gujranwala (2015)
  • Find the equation of hyperbola with centre (0,0), focus (6,0) and vertex (4,0). — BSIC Gujranwala (2015)
  • Prove that the line segment joining the mid-points of two sides of a triangle is parallel to third side and half as long. — BSIC Gujranwala (2015)
  • Find focus, vertex and directrix of parabola x2−4x−8y+4=0 — BSIC Gujranwala (2015)
  • Find the equations of two tangents drawn from (2,3) to the circle x2+y2=9.— FBSIC (2017)
  • Find the foci, eccentricity and vertices of an ellipse (2x−1)216+(y+2)216=1 — FBSIC (2017)
  • Find the equations of tangents to the conic 9x2−4y2=36 and parallel to the 5x−2y+7=0 — FBSIC (2017)
  • Prove that the altitudes of a triangle are constant. — FBSIC (2017)
  • Find the equation of the circle whose ends of diameter at (−3,2) and (5,−6)..— FBSIC (2016)
  • Find an equation of the parabola whose focus is F(−3,4) and directrix is 3x−4y+5=0. .— FBSIC (2016)
  • Find the point of intersection of the given conic 3x2−4y2 and 3y2−2x4=7. .— FBSIC (2016)
  • Let α be a positive number and 0<c<a. Let F(c,0) and F‘(−c,0) be two given points. Prove that the locus of points P(x,y) such that |PF|+|PF‘|=2a is an ellipse. — FBSIC (2016 )
  • Find the centre and radius of the circle 5x2+5y2+14x+12y−10=0.— BSIC Rawalpandi(2017 )
  • Determine whether the point P(−5,6) lies outside on or inside the circle x2+y2+4x−6y−12=0— BSIC Rawalpandi(2017 )
  • Find focus and vertex of parabola y2=−8(x−3). — BSIC Rawalpandi(2017 )
  • Find the foci and eccentricity of an ellipse 25x2+9y2=225.— BSIC Rawalpandi(2017 )
  • Show that the lines 3x−2y=0 and 2x+3y−13=0 are tangent to the circle x2+y2+6x−4yy=0.— BSIC Rawalpandi(2017 )
  • Find centre, foci and vertices of the hyperbola (x−1)22−(y−1)29=1 — BSIC Rawalpandi(2017 )
  • Find the equation of the line represented by 20x2+17xy−24y2=0 — BSIC Sargodha(2016)
  • Find the centre and radius of the circle 4x2+4y2−8x+12y−25=0— BSIC Sargodha(2016)
  • Find the length of the tangent from the point P(−5,10) to the circle 5x2+5y2+14x+12y−10=0— BSIC Sargodha(2016)
  • Find the coordinates of foci and vertices of ellipse 25x2+9y2=225— BSIC Sargodha(2016)
  • Find the foci and eccentricity of the hyperbola y216−x249=1 — BSIC Sargodha(2016)
  • Find the coordinates of the points of intersection of the line x+2y=6 with the circle x2+y2−2x−2y−39=0— BSIC Sargodha(2016)
  • Prove that in any triangle ABC, b2=c2+a2−2cacosB– BSIC Sargodha(2016)
  • Find focus and vertex of x2=−16y.— BSIC Sargodha(2017)
  • Find eccentricity of ellipse x22+y218=1.— BSIC Sargodha(2017)
  • Define vertices and co-vertices of an ellipse.— BSIC Sargodha(2017)
  • Find focus, vertex and directrix of x+8−y2+2y=0 .— BSIC Sargodha(2017)
  • Find the points of intersection of the conic y=1+x2 and y=1+4x−x2.— BSIC Sargodha(2017)
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