Maths · Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms
Triangle is inscribed in the parabola described by the equation so that is the v
Triangle \( A B C \) is inscribed in the parabola described by the equation \( y^{2}-6 x-4 y+10=0 \) so that \( A \) is the vertex of the parabola and \( B \) and \( C \) are the end points of the latus rectum of the parabola. The area of triangle \( A B C \) is
- A. 18
- B. 9
- C. 4 .5 \)
- D. 2.25
Step-by-step solution
Rewrite the parabola equation as (y-2)^2 = 6(x-1). Vertex A is (1,2), a=1.5, focus (2.5,2). Latus rectum endpoints B(2.5,5) and C(2.5,-1). Base BC length = 6, height from A to line x=2.5 is 1.5, area = 0.5*6*1.5 = 4.5.
Related MCQs
- and are fixed points. If is a constant, locus of is…
- Arrange in the descending order of the values: A: If (9,12) is one end of a focal chord of the parabola then the slope of it is B: The parab…
- if the distance between the foci is equal to the length of the latus-rectum. Find the eccentricity of the ellipse.…
- The sum of the focal distances of a point on the ellipse is:…
- The function is defined by = \) (x+1) \) The graph of in the plane is a parabola.Which of the following intervals contains the coordinate of…