WBJEE · Maths · Straight Lines
Aline cuts the \(x\) -axis at \(A(7,0)\) and the \(y\) -axis at \(B(0,-5)\). A variable line \(P Q\) is drawn perpendicular to \(A B\) cutting the \(x\) -axis at \(P(a, 0)\) and the \(y\) -axis at \(Q(0, b)\). If \(A Q\) and BP intersect at \(R\), the locus of \(R\) is
- A \(x^{2}+y^{2}+7 x+5 y=0\)
- B \(x^{2}+y^{2}+7 x-5 y=0\)
- C \(x^{2}+y^{2}-7 x+5 y=0\)
- D \(x^{2}+y^{2}-7 x-5 y=0\)
Answer & Solution
Correct Answer
(C) \(x^{2}+y^{2}-7 x+5 y=0\)
Step-by-step Solution
Detailed explanation
Hint: \(\mathrm{P}\) is orthocentre of \(\triangle \mathrm{ABQ}\) \(\mathrm{m}_{\mathrm{BR}} \times \mathrm{m}_{\mathrm{AR}}=-1\) \(\Rightarrow\left(\frac{\mathrm{k}+5}{\mathrm{~h}}\right) \times\left(\frac{\mathrm{k}}{\mathrm{h}-7}\right)=-1\)…
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