# Rectangular and Cartesian products Questions and answers

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31). lf every point on the line $$\Large \left(a_{1}-a_{2}\right)x+ \left(b_{1}-b_{2}\right)y=c$$ is equidistant from the points $$\Large \left(a_{1},\ b_{1}\right)$$ then 2c is equal to:
 A). $$\Large a^{2}_{1}+b^{2}_{1}+a^{2}_{2}-b^{2}_{2}$$ B). $$\Large a^{2}_{1}+b^{2}_{1}+a^{2}_{2}+b^{2}_{2}$$ C). $$\Large a^{2}_{1}+b^{2}_{1}-a^{2}_{2}-b^{2}_{2}$$ D). none of these
32). If two vertices of a triangle are $$\Large \left(-2,\ 3\right)\ and\ \left(5,\ -1\right)$$ orthocentre lies at origin and centroid on the line x + y = 7, then the third vertex lies at:
 A). $$\Large \left(7,\ 4\right)$$ B). $$\Large \left(8,\ 14\right)$$ C). $$\Large \left(12,\ 21\right)$$ D). none of these
33). The locus of a points p which moves such that 2PA = 3PB, where $$\Large A \left(0,\ 0\right)\ and\ B \left(4,\ -3\right)$$ are points is:
 A). $$\Large 5x^{2}-5y^{2}-72x+54y+225=0$$ B). $$\Large 5x^{2}+5y^{2}-72x+54y+225=0$$ C). $$\Large 5x^{2}+5y^{2}+72x-54y+225=0$$ D). $$\Large 5x^{2}+5y^{2}-72x-54y+225=0$$
34). If $$\Large A \left(-a,0\right)$$ and $$\Large B \left(a,0\right)$$ are two fixed points, then the locus of the point at which AB subtends a right angle is;
 A). $$\Large x^{2}+y^{2}=2a^{2}$$ B). $$\Large x^{2}-y^{2}=a^{2}$$ C). $$\Large x^{2}+y^{2}+a^{2}=0$$ D). $$\Large x^{2}+y^{2}=a^{2}$$
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