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The variable line y = k*x + h is tangent to the hyperbola x²/4 - y²/9 = 1. If the locus of the point P(h, k) is a conic, which of the following is true?

1. the centre of the conic is at the origin
2. the focus of the conic lies on the y-axis
3. the eccentricity of the conic exceeds that of the given hyperbola
4. the conic is an ellipse

Correct answer: the centre of the conic is at the origin

Solution

The condition c² = a²*m² - b² gives h² = 4k² - 9, i.e. 4k² - h² = 9, a hyperbola centred at the origin.

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