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.

True

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False

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Solution

The correct option is A
True

The given statement is the definition of a conic. Most of the time, the statements starts with "ratio of distance from a fixed point a to . . . . . .”. Here we are taking the reciprocal of the ratio. If the ratio is a constant, then the reciprocal of that will also be constant.

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Similar questions

A conic section is a locus of a point P which moves in such a way that its distance from a fixed point S always bears a constant ratio to its distance from a fixed line, all being in the same plane. The fixed point is called …… and the fixed line is called ……

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.

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}

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}

Q. A point in the space moves such that the ratio of its distances from two fixed points is a constant

(\neq 1)

, then the locus is

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