MathDB

Problem 4

Part of 2019 LIMIT Category B

Problems(2)

graph of equation

Source: LIMIT 2019 CBS1 P4

4/28/2021
The equation x3y+xy3+xy=0x^3y+xy^3+xy=0 represents <spanclass=′latex−bold′>(A)</span> a circle<span class='latex-bold'>(A)</span>~\text{a circle} <spanclass=′latex−bold′>(B)</span> a circle and a pair of straight lines<span class='latex-bold'>(B)</span>~\text{a circle and a pair of straight lines} <spanclass=′latex−bold′>(C)</span> a rectangular hyperbola<span class='latex-bold'>(C)</span>~\text{a rectangular hyperbola} <spanclass=′latex−bold′>(D)</span> a pair of straight lines<span class='latex-bold'>(D)</span>~\text{a pair of straight lines}
geometryalgebra
find locus with angle condition

Source: LIMIT 2019 CBS2 P4

4/28/2021
A particle PP moves in the plane in such a way that the angle between the two tangents drawn from PP to the curve y2=4axy^2=4ax is always 90∘90^\circ. The locus of PP is <spanclass=′latex−bold′>(A)</span> a parabola<span class='latex-bold'>(A)</span>~\text{a parabola} <spanclass=′latex−bold′>(B)</span> a circle<span class='latex-bold'>(B)</span>~\text{a circle} <spanclass=′latex−bold′>(C)</span> an ellipse<span class='latex-bold'>(C)</span>~\text{an ellipse} <spanclass=′latex−bold′>(D)</span> a straight line<span class='latex-bold'>(D)</span>~\text{a straight line}
geometry