wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The ratio of the area of a triangle inscribed in a parabola to the area of the triangle formed by the tangents drawn at the vertices of the triangle is

A
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2.00
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2.0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

Let the parabola be y2=4ax
Assuming the points of the triangle be A,B,C as
(at21,2at1),(at22,2at2),(at23,2at3) respectively.

Let P,Q,R be the points of intersection of tangents at B,C; C,A; A,B
P=(at2t3,a(t2+t3))
Similarly,
Q=(at1t3,a(t1+t3))R=(at2t1,a(t2+t1))

Area of
ABC=12∣ ∣ ∣at212at11at222at21at232at31∣ ∣ ∣applying R1R1R3 R2R2R3=a2∣ ∣ ∣t21t23t1t30t22t23t2t30t23t31∣ ∣ ∣=a2|(t1t2)(t2t3)(t1t3)|

Area of
PQR=12∣ ∣ ∣at3t2a(t2+t3)1at3t1a(t3+t1)1at1t2a(t1+t2)1∣ ∣ ∣applying R1R1R2 R2R2R3=a22∣ ∣ ∣t3(t2t1)(t2t1)0t1(t3t2)(t3t2)0t1t2(t1+t2)1∣ ∣ ∣=a22|(t1t2)(t2t3)(t1t3)|2PQR=ABC

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
x^2 - y^2
Watch in App
Join BYJU'S Learning Program
CrossIcon