Question

A, B, C, D are the points of intersection with the co-ordinate axes of the lines $ax+by=ab$ and $bx+ay=ab$ then

• A. A, B, C, D are concyclic
• B. A, B, C, D forms a parallelogram
• C. A, B, C, D forms a rhombus
• D. none of these

Answer 1

The correct option is A A, B, C, D are concyclic

At $y=0$

$ax=ab\Rightarrow x=b$

and,

$bx=ab\Rightarrow x=a$

$A(b,0)$ and $C(a,0)$

At $x=0$

$by=ab\Rightarrow y=a$

and,

$ay=ab\Rightarrow y=b$

$B(0,a)$ and $D(0,b)$

Any $3$ points among $A,B,C,D$ do not lie in a single line.

Hence, $AB$ and $CD$ can be chords or diameter of a circle

Hence, $A,B,C,D$ are concylic points.