Please help me with 20th sum correct answer is 10 - Maths - Conic Sections

Question

Please help me with 20th sum

correct answer is 10

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

xy=c c>0        
ix2+y2=25         
iiFrom i and ii, we getcy2+y2=25⇒c2y2+y2=25⇒c2+y4=25y2⇒y4+25y2+c2=0     
iThis means, y can have maximum of four values i
e
 the number of point of intersection can be maximum 4
But it is given that the point of intesection is two
⇒The equation must have two equal roots
So, D=0⇒252-4×1×c2=0⇒625-4c2=0⇒c2=6254⇒c=252     c>0So, using i, we gety4+25y2+6254=0           ⇒y22+2×y2×252+2522=0⇒y2+2522=0⇒y2=252⇒y=±52If y=-52,thenx=cy=252-52⇒x=-52If y=52,thenx=cy=25252⇒x=52So, the two point of intersection are A-52,-52 and B52,52
Now, the distance AB=52+522+52+522=1022+1022=21022=21022=102∴ AB=10 units

Hope
this
information will clear
your doubts about the
topic
Regards