Conic Sections

The correct option is (C): (3 4), (- 13, 4)
Given that



where
The ends of the latus rectum are (2 A, A) and (-2 A, A)
and x+5=-2(4)

Given : ellipse equation :
Circle equation :
center of ellipse

length of major axis is
length of minor is
center of circle is with radius
so, wecanseeindiagramthatthetwoareasdoesnotintersectortoucheachlengthiso
Hence, The length of common chord of the ellipse and circle is Zero(o).

Step 1: Formula for Latus Rectum For a hyperbola, the length of the latus rectum is given by: We are given: Step 2: Using the Eccentricity Formula The eccentricity of a hyperbola is given by: We are given: From the standard hyperbola relation: Step 3: Expressing and From , we express as: Rearrange the standard relation: Expanding: Rearrange: Step 4: Solving for Using the latus rectum equation: Substituting : Simplify: Solving for : Step 5: Finding Transverse Axis Length The transverse axis length is: Thus, the correct answer is , which matches option (C).