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Co-ordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCo-ordinate Geometry1 Mark
MCQ
If points $A\left(a^2, 0\right), B\left(0, b^2\right)$ and $C(1,1)$ are collinear, then
  • ✓
    $\frac{1}{a^2}+\frac{1}{b^2}=1$
  • B
    $\frac{1}{a}+\frac{1}{b}=1$
  • C
    $a^2+b^2=1$
  • D
    $\frac{1}{a^2}+\frac{1}{b^2}=2$
✓

Answer

Correct option: A.
$\frac{1}{a^2}+\frac{1}{b^2}=1$
(A)$\frac{1}{a^2}+\frac{1}{b^2}=1$
Given points are collinear.
$\frac{a^2-0}{a^2-1}=\frac{0-b^2}{0-1} \qquad\left[\right.$ Using $\left.: \frac{x_1-x_2}{x_1-x_3}=\frac{y_1-y_2}{y_1-y_3}\right]$
$\Rightarrow \quad a^2=b^2\left(a^2-1\right) \Rightarrow a^2+b^2=a^2 b^2 \Rightarrow \frac{1}{a^2}+\frac{1}{b^2}=1$

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