Flag Analytical Geometry> CIRCLES...
question mark

1)Find the sum of integral values of m for which the line y=mx+4 cuts circle x2+y2-4x=32 but not circle x2+y2=4

Vatsal Koradia , 13 Years ago
Grade 11
anser 1 Answers
mathew jacob

Last Activity: 13 Years ago

the circle x2 + y2 = 4 is in the interior of the the other circle

now crawing approx graph we can see that the y intercept of the small circle is +2or -2 however we are interested only in +2

and the big cicle has y intercept +4*2^1/2  and hence we can infer that the line y = mx + 4 is a line that rotates between the y intercepts of the two circles since the y intercept of this line is +4.

now going into the integral solutions m=0 is obviously a solun as it does not cut the small circle

an important point here is tha for all values of m the line will cut th big circle .

now putting m=1,2,3 we can see that for 1&2 by solving the two equations we see that the line intersects the small circle at no point . but for 3 it cuts th circle as D(discriminant )>0 for this case and hence for all higher values it will cut the small circle .

s our positive solutions are 1&2

now moving to the negative m by pure logic we can argue that as the small circle and the line are symmetrical about the y axis and keeping in mind the very important fact that for all values of m line cuts the big circle   we can conclude that the same nos. comes in the other side also that is the negative solutions are -1&-2.

 

now we have 5 solutions -2,-1,0,1,2 and the sum is clearly 0

thank you

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...