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

Consider the two curves C1:y2=4x, C2:x2+y2−6x+1, then

A
C1 and C2 touch each other only at one point.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
C1 and C2 touch each other exactly at two points
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
C1 and C2 intersect (but do not touch) at exactly two points,
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
C1 and C2 neither intersect nor touch each other.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B C1 and C2 touch each other exactly at two points
Solving the two equations, we get
x2+4x6x+1=0
x2+2x+1=0
x=1 and y=±2
So the two curves meet at two points (1,2) and (1,2).
Equation of the tangent at (1,2) to C1 is y(2)=2(x+1)
y=x+1
and Equation of the tangent at (1,2) to C2 is
x.1+y(2)3(x+1)+1=0y=x+1
Showing that C1 and C2 have a common tangent at the point (1,2).
Similarly they have a common tangent
y=(x+1)at(1,2)
Hence, the two curves touch each other exactly at two points.
222940_195087_ans_bb3f59830031407394f3bbe5c2d355fb.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Area under the Curve
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon