AP EAMCET · Maths · Straight Lines
\(A(-2,3)\) is a point on the line \(4 x+3 y-1=0\). If the points on the line that are 10 units away from the point \(A\) are \(\left(x_1, y_1\right)\) and \(\left(x_2, y_2\right)\), then \(\left(x_1+y_1\right)^2+\) \(\left(x_2+y_2\right)^2=\)
- A \(10\)
- B \(90\)
- C \(180\)
- D \(405\)
Answer & Solution
Correct Answer
(A) \(10\)
Step-by-step Solution
Detailed explanation
The direction vector of the line \(4x+3y-1=0\) is \((3, -4)\). Unit direction vector: \(\left(\cos\theta, \sin\theta\right) = \left(\frac{3}{\sqrt{3^2+(-4)^2}}, \frac{-4}{\sqrt{3^2+(-4)^2}}\right) = \left(\frac{3}{5}, -\frac{4}{5}\right)\). Points on the line 10 units away from…
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