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Course: Algebra (all content)>Unit 17

Lesson 12: Challenging conic section problems (IIT JEE)

Intersection of circle & hyperbola

2010 IIT JEE Paper 1 Problem 46: Find the equation of a circle whose diameter is defined by the two intersection points of given circle and hyperbola. Created by Sal Khan.

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• I must have missed it somewhere, why we need to complete the square at the start? for the circle equation? whats the reason behind it?
• It's to put the equation in the standard form to make the radius clear.
• at Mr.Khan adds 16 to the left but adds 6 to the left
and my math teacher says whatever you do to the left you have to do to the right...?

or nawwwww
• That was most certainly a written error. It doesn't affect the rest of the question because he continued the addition correctly.
• At , Sal dismissed a negative extraneous root of x. How was that extraneous root created? I was curious because I did not see Sal square both sides of an equation or do anything else that would produce a false root.
• he does not need the negative root
the intersection is on right side of y axis
• fast solution: first, look at the choices, then graph both of them, look at the intersection points, predict the y and x from looking at it, and then substitute for the equation of the circle. expand... you choose the answer closest to yours.
• How did Sal get the 4 points that made the circle in the first part of the video?
• He used the equation of the circle that was already given.
• How do we know that the center was (6,0)?. I understood the equation that he did was for the points in the circle not for the center. Help please!
(1 vote)
• The midpoint of the diameter (center of circle) with end points (6, root 12) and (6, - root 12) would give (6, 0)
• but we just found the positive slope of the hyperbola not the negative one.so at how would sal prove the other line from the equation of the hyperbola.when he seid " And it's going to be symmetric ".
(1 vote)
• what if x is not a pretty number like 15plus or minus square root of 305 divided by 10?
(1 vote)
• They are probably not going to give a question like this which does not result in relatively simple values of x.
(1 vote)
• How do you know to Solve for y^2? I tried making the equation of the circle and the hyperbola equal to 1 and then setting them equivalent, which got me to a dead end at 7x^2 + 72x - 45y^2 = 0. I understand the tools we're being taught, but I'm struggling with how to strategically solve a problem. I'm just blindly algebraically manipulating things and going in circles or dead-ending.
(1 vote)
• This is OT but I have a problem anwering the questions about rectangular forms of complex numbers when i write : 14sqrt[cos 135° + i sin 135°] the program tells me that it doesn't understand I used ALT+248, ALT 0176 and ALT 0186 to make the "degree" sign.
But the program still doesn't understand.
What am I doing wrong?
(1 vote)
• Don't use the degree sign. Just put it in manually like cos(135). If you need to, convert the degrees to radians first.
(1 vote)