Coordinate geometry 2 questions | form six Pure Advanced Mathematics

(6631) Question Category: Mathematical Calculation

Find the equation of a tangent to the ellipse 4x2+y2=6 at (frac{1}{2}, sqrt{5}) in the form ax+by+c=0.

Answer / Solution

UNSOLVED

(6632) Question Category: Mathematical Calculation

The points P(at_{1}^{2},2at_{1}) and Q(at_{2}^{2},2at_{2}) lie on the parabola y^{2}=4ax. The tangents at the points P and Q intersect at R. Find the coordinates of R.

Answer / Solution

UNSOLVED

(6633) Question Category: Mathematical Calculation

Convert the following polar equations into Cartesian equations:

  1. r^{2}=4sin2 heta
  2. r=3(1+cos heta)

Answer / Solution

UNSOLVED

(6634) Question Category: Mathematical Calculation

A curve is defined by the parametric equations x=t^{2} and y=frac{2}{t} where t eq 0. Show that the equation of the normal at the point Qleft ( p^{2} ,frac{2}{p^{2}} ight ) is p^{4}x-py+2=p^{6}.

Answer / Solution

UNSOLVED

(6635) Question Category: Mathematical Calculation

Show that the equation of a tangent to parabola y^{2}=4ax at point (x_{1},y_{1}) is yy_{1}=2a(x+x_{1}).

Answer / Solution

UNSOLVED

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