Which of the following describes a conic?

Here S is a fixed point and P is the moving point. 'e' is the eccentricity of the conic

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

We will derive this from the definition of a conic. A conic section is defined as the locus of a point. The point satisfies the following condition. Its ratio of distance from focus (fixed point) to the perpendicular distance of that point from directrix (fixed line) is constant. That constant is the eccentricity e.

Distance from focus = $P S$

Perpendicular distance from Line = $P M$

Ratio =e $\Rightarrow \frac{P S}{P M} = e$

Suggest Corrections

Similar questions

Which of the following describes a conic?

Here S is a fixed point and P is the moving point. 'e' is the eccentricity of the conic

Point of intersection of the lines $\sqrt{3} x - y - 4 \sqrt{3} m = 0$ and $\sqrt{3} m x + m y - 4 \sqrt{3} = 0$ describes-

If a curve passing through P(4, 2) and satisfies the differential equation $\frac{d y}{d x} = \frac{y}{x - y^{2}}$ is a conic then which of the following is correct?

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. Point of intersection of the lines

\sqrt{3 x} - y - 4 \sqrt{3 m} = 0

and

\sqrt{3} m x + m y - 4 \sqrt{3} = 0

describes

Join BYJU'S Learning Program