54. A fixed point is at a perpendicular distance 'a' from a fixed straight line and a point moves so that its distance from the fixed point is always equal to its distance from the fixed line.Find the equation to its locus , the Axis of coordinates being drawn through the fixed point and being parallel and perpendicular to the given line.

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Q. A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that its distance from the fixed point is always equal to its distance from the fixed line. Find the equation to its locus, the axes of coordinates being drawn through the fixed point and being parallel and perpendicular to the given line.

Q. A fixed point is at a perpendicular distance

a

from a fixed straight line and a point moves so that its distance from the fixed point is always equal to its distance from the fixed line. The axes of coordinates being drawn through the fixed point and being parallel and perpendicular to the given line.

If the first distance be (1) always half and (2) always twice the second distance, find the equations to the respective loci.

Q. Find the locus of a point which moves so that the difference of its distances from two fixed straight lines at right angles is equal to its distance from a fixed straight line.

Match the columns by referring to the definition given below.

"A conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed straight line”.

\begin{matrix} Definition & Name P) Fixed point & 1. Axis Q) Fixed straight line & 2. Vertex R) Constant ratio & 3. Directrix S) Line passing through fixed point and perpendicular to fixed line & 4. Focus 5. Eccentricity \end{matrix}

A conic is the locus of a point such that its ratio of perpendicular distance from a fixed line to its distance from a fixed point is a constant.

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