I am reading linear algebra and there is a problem involving hyperbolic curves that struggle with.
Three points $P_0=(0,0), P_1=(0,\frac{21}{4}), P_2=(0,\frac{25}{3})$. A point is located $\frac{5}{3}$ units closer to $P_0$ than $P_2$, and $\frac{7}{4}$ units closer to $P_1$ than $P_0$. What is this points coordinates?
I have come to two hyperbolic curves between $P_0, P_1$ and $P_0, P_2$: $$(8y-21)^2-8x^2=7^2$$ $$(6x-25)^2-\frac{3y^2}{2}=5^2$$
However when I try to solve for the intersection all I get is a complicated fourth degree polynomial. I must be taking the long road to solve this or maybe my brain is fried today. Please help!
The book answer: $(3,4)$