Solve this: Area of the trapezium whose vertices lie on the parabola y2 = 4x and its diagonals pass through - Maths - Matrices

Question

Solve this:
Area of the trapezium whose vertices lie on the parabola
y2 = 4x and its diagonals pass through (1, 0) and having
length 25 4 unit each, is
A) 75 4 sq unit B) 625 16 sq unit C) 25 4 sq unit D) 25 8 sq unit

Abhishek Kr. Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
Let A,B,C and D are vertices of trapezium
Focus of the parabola y2=4x is (1,0)So diagonals are focal chordAS=1+t2=m (Let)1m+1254-m=1   {since 1AS+1CS=1a}⇒254=254m-m2⇒4m2-25m+25=0⇒m=54 or 5For m=54 ⇒1+t2=54 ⇒t2=54-1=14⇒t=±12For m=5⇒1+t2=5⇒t2=5-1=4⇒t=±2So, coordinates of A, B, C and D are A 14,1; B 4,4, C4,-4 and D 14,-1AD=2 and BC=8So, distance between AD and BC = 154So, area of trapezium ABCD = 122+8×154=754 sq
 units
Regards

Solve this: Area of the trapezium whose vertices lie on the parabola y2 = 4x and its diagonals pass through (1, 0) and having length 25 4 unit each, is A) 75 4 sq. unit B) 625 16 sq. unit C) 25 4 sq. unit D) 25 8 sq. unit

Solve this:
Area of the trapezium whose vertices lie on the parabola y² = 4x and its diagonals pass through (1, 0) and having length $\frac{25}{4}$ unit each, is
A) $\frac{75}{4}$ sq. unit B) $\frac{625}{16}$ sq. unit C) $\frac{25}{4}$ sq. unit D) $\frac{25}{8}$ sq. unit