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10-2. Parabola, Ellipse, Hyperbola
hard
If $A = [(x,\,y):{x^2} + {y^2} = 25]$ and $B = [(x,\,y):{x^2} + 9{y^2} = 144]$, then $A \cap B$ contains
A
One point
B
Three points
C
Two points
D
Four points
Solution
(d) $A = $ Set of all values $(x, y) :$ ${x^2} + {y^2} = 25 = {5^2}$
$B = {{{x^2}} \over {144}} + {{{y^2}} \over {16}} = 1$ i.e., ${{{x^2}} \over {{{(12)}^2}}}$ + ${{{y^2}} \over {{{(4)}^2}}} = 1$.
Clearly, $ A \cap B $ consists of four points.
Standard 11
Mathematics
