MCQ
The points $( - a, - b),\;(a,b),\;({a^2},ab)$are
- AVertices of an equilateral triangle
- BVertices of a right angled triangle
- CVertices of an isosceles triangle
- ✓Collinear
${l_2} = \sqrt {{{({a^2} - a)}^2} + {b^2}{{(a - 1)}^2}} = (a - 1)\,\sqrt {{a^2} + {b^2}} $
${l_3} = \sqrt {{{({a^2} + a)}^2} + {b^2}{{(a + 1)}^2}} = (a + 1)\,\sqrt {{a^2} + {b^2}} $
Now ${l_1} + {l_2} = {l_3}.$ Hence points are collinear.
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$x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R$
consider the following statements :
$(A)$ The system has unique solution if $k \neq 2$, $k \neq-2$
$(B)$ The system has unique solution if $k =-2$.
$(C)$ The system has unique solution if $k =2$.
$(D)$ The system has no-solution if $k =2$.
$(E)$ The system has infinite number of solutions if $k \neq-2$
Which of the following statements are correct?