First slide

Equation of line in Straight lines

Question

The coordinate axes are rotated about the origin ‘O’ in the counter clockwise direction through an angle 60^o. If a and b are the intercepts made on the new axes by a straight line whose equation referred to the original axes is 3x + 4y-5=0 then $\frac{1}{a^{2}} + \frac{1}{b^{2}} =$

Moderate

Solution

$p = \frac{5}{3}, q = \frac{5}{4}, \frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{p^{2}} + \frac{1}{q^{2}}$ = $\frac{9}{25} + \frac{16}{25} = 1$

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