Question

The locus of the point of intersection of the lines xcosα + ysinα = α and xsinα – ycosα = b(where α is a variable) is ______.

Options

• x² + y² = a² + b²

• x² - y² = a² + b²

• x² + y² = a² – b²

• x² – y² = a² – b²

Answer 1

The locus of the point of intersection of the lines xcosα + ysinα = α and xsinα – ycosα = b(where α is a variable) is `underlinebb(x^2 + y^2 = a^2 + b^2)`.

Explanation:

xcosα + ysinα = α  ......(1)

xsinα – ycosα = b  ......(2)

On squaring (1) and (2), then adding, we get

x²cos²α + y²sin²α + 2xy sinα cosα + x²sin²α + y²cos²α – 2xy sinα cosα = a² + b²

⇒ x²(sin²α + cos²α) + y²(sin²α + cos²α) = a² + b²

⇒ x² + y² = a² + b²