1999 - JAMB Mathematics Past Questions and Answers - page 3

The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.

PV = PW

(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}

• (y-5)^{2}}).
  
  

Squaring both sides of the equation,

(x-1)² + (y-1)² = (x-3)² + (y-5)².

x²-2x+1+y²-2y+1 = x²-6x+9+y²-10y+25

Collecting like terms and solving, x + 2y = 8.

(y = x(2-x) \Rightarrow y= 2x - x^{2};

\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\

solving further gives (4 - \frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit)

(y = 2x \ V = \int\pi^{2}dy \ but\hspace{1mm}y = 2x \ V = \int\pi4x^{2}dx\ V = \frac{4(3)^{3}\pi}{3}-\frac{4(3)^{3}\pi}{3}\V=\frac{4*27\pi}{3} = 36\pi \hspace{1mm}cubic\hspace{1mm}units)

t² sin (3t - 5) = 2t sin ( 3t - 5) + t² x 3 cos (3t - 5) = 2t sin (3t - 5) + 3t² cos (3t - 5).

Detailed answer below was provided by Ifechuks, a female prospective student of Okopoly.