ENH: Add option for `to_json` function to discard null values
#### Is your feature request related to a problem?

No, at least not that I am aware of.

#### Describe the solution you'd like

The [documentation](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.to_json.html) states that "NaN’s and None will be converted to null" when using `pandas.DataFrame.to_json`. I'd like to have an option for the `to_json` function, so that keys that have a null value will be discarded. See "'Additional context" for an example.

#### API breaking implications

New optional parameter for `pandas.DataFrame.to_json`. However by default this option should be disabled, so no breaking implications, I think.

#### Additional context

``` python
import pandas as pd
import numpy as np

data = {
    # None and np.nan will result in null values when converting to JSON
    "a": [None, 1, 2],
    "b": [0, np.nan, 0]
}
df = pd.DataFrame(data)

# Note: `discard_null` doesn't exist yet
print(df.to_json(orient="records", discard_null=True))

# current result: [{"a":null,"b":0.0},{"a":1.0,"b":null},{"a":2.0,"b":0.0}]
# desired result: [{"b":0.0},{"a":1.0},{"a":2.0,"b":0.0}]
```

Currently I am only working with `orient="records"`. Does it make sense to restrict the option only to this orientation or does it make sense to implement this option for other orientations as well?

I'd like to implement this feature by myself and contribute a PR. If there are any tips about how I can do this, please let me know 👌 